business statistics . In this chapter, you learn:
To construct and interpret confidence interval estimates for the population mean
To determine the sample size necessary to develop a confidence interval for the population mean
A point estimate is a single number,
a confidence interval provides additional information about the variability of the estimate
Suppose confidence level = 95%
Also written (1 - ) = 0.95, (so = 0.05)
A relative frequency interpretation:
95% of all the confidence intervals that can be constructed will contain the unknown true parameter
A specific interval either will contain or will not contain the true parameter
No probability involved in a specific interval. A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
Determine a 95% confidence interval for the true mean resistance of the population.
A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
We are 95% confident that the true mean resistance is between 1.9932 and 2.4068 ohms
Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean
Interpreting this interval requires the assumption that the population you are sampling from is approximately a normal distribution (especially since n is only 25).
This condition can be checked by creating a:
Normal probability plot or
Boxplot
The required sample size can be found to reach a desired margin of error (e) with a specified level of confidence (1 - )
The margin of error is also called sampling error
the amount of imprecision in the estimate of the population parameter
the amount added and subtracted to the point estimate to form the confidence interval
This document provides an overview of sampling distributions and the central limit theorem. It begins with definitions of key terms like population, sample, and sampling distribution. It then demonstrates how to develop a sampling distribution by considering all possible samples from a population. The document explains that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, even if the population is not normally distributed, according to the central limit theorem. It provides examples of how to calculate probabilities related to sampling distributions.
This chapter discusses sampling and sampling distributions. It covers different sampling methods like simple random sampling, stratified sampling, and cluster sampling. The key concepts explained are sampling frame, sampling distribution, standard error of the mean, and the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normally distributed.
This chapter discusses sampling and sampling distributions. The key points are:
1) A sample is a subset of a population that is used to make inferences about the population. Sampling is important because it is less time consuming and costly than a census.
2) Descriptive statistics describe samples, while inferential statistics make conclusions about populations based on sample data. Sampling distributions show the distribution of all possible values of a statistic from samples of the same size.
3) The sampling distribution of the sample mean is normally distributed for large sample sizes due to the central limit theorem. Its mean is the population mean and its standard deviation decreases with increasing sample size. Acceptance intervals can be used to determine the range a
This chapter discusses sampling and sampling distributions. It introduces key concepts such as populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains that sampling distributions describe the distribution of all possible values of a statistic from samples of a given size. The chapter focuses on the sampling distributions of the sample mean and sample proportion. It derives the formulas for the mean and standard deviation of the sampling distribution of the sample mean. It also discusses the central limit theorem and how large sample sizes cause sampling distributions to approach a normal distribution regardless of the shape of the population.
This chapter discusses sampling and sampling distributions. It aims to describe simple random sampling, explain the difference between descriptive and inferential statistics, define sampling distributions, and determine properties of key sampling distributions such as the mean, proportion, and variance. The key points are:
- Sampling distributions describe the distribution of all possible values of a statistic from samples of a given size from a population.
- The sampling distribution of the mean is normally distributed for large samples, with mean equal to the population mean and standard deviation equal to the population standard deviation over the square root of the sample size.
- Even if the population is not normal, the Central Limit Theorem states that the sampling distribution of the mean will be approximately normal for large
This document provides an overview of sampling and sampling distributions. It begins by stating the chapter goals, which are to describe key sampling concepts like simple random samples and explain the differences between descriptive and inferential statistics. It then defines important terms like population, sample, and sampling distribution. The document explains that sampling is used instead of censuses because it is less time-consuming and costly while still providing sufficiently precise results. It also outlines the chapter, noting it will cover the sampling distributions of the sample mean, sample proportion, and sample variance. It provides examples of how to determine the properties of these sampling distributions such as their means and standard deviations. It emphasizes the central limit theorem and how large samples lead to normally distributed sampling distributions even
This document provides an overview of sampling and sampling distributions. It defines key concepts like populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains how sampling distributions are developed and their properties. Specifically, it discusses the sampling distribution of the sample mean, including how it has an expected value equal to the population mean and standard error that decreases as sample size increases. The Central Limit Theorem is also summarized, stating that as sample size increases, the sampling distribution will approach a normal distribution regardless of the shape of the original population.
This chapter discusses sampling distributions and their properties. It covers the sampling distribution of the mean and the proportion. The key points are:
- A sampling distribution describes the distribution of a statistic like the mean from random samples of a population.
- The Central Limit Theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normal.
- For the mean, the sampling distribution has a mean equal to the population mean and standard deviation that decreases as sample size increases.
- For a proportion, the sampling distribution can be approximated as normal if sample size n and np or n(1-p) are large enough.
This document provides an overview of sampling distributions and the central limit theorem. It begins with definitions of key terms like population, sample, and sampling distribution. It then demonstrates how to develop a sampling distribution by considering all possible samples from a population. The document explains that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, even if the population is not normally distributed, according to the central limit theorem. It provides examples of how to calculate probabilities related to sampling distributions.
This chapter discusses sampling and sampling distributions. It covers different sampling methods like simple random sampling, stratified sampling, and cluster sampling. The key concepts explained are sampling frame, sampling distribution, standard error of the mean, and the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normally distributed.
This chapter discusses sampling and sampling distributions. The key points are:
1) A sample is a subset of a population that is used to make inferences about the population. Sampling is important because it is less time consuming and costly than a census.
2) Descriptive statistics describe samples, while inferential statistics make conclusions about populations based on sample data. Sampling distributions show the distribution of all possible values of a statistic from samples of the same size.
3) The sampling distribution of the sample mean is normally distributed for large sample sizes due to the central limit theorem. Its mean is the population mean and its standard deviation decreases with increasing sample size. Acceptance intervals can be used to determine the range a
This chapter discusses sampling and sampling distributions. It introduces key concepts such as populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains that sampling distributions describe the distribution of all possible values of a statistic from samples of a given size. The chapter focuses on the sampling distributions of the sample mean and sample proportion. It derives the formulas for the mean and standard deviation of the sampling distribution of the sample mean. It also discusses the central limit theorem and how large sample sizes cause sampling distributions to approach a normal distribution regardless of the shape of the population.
This chapter discusses sampling and sampling distributions. It aims to describe simple random sampling, explain the difference between descriptive and inferential statistics, define sampling distributions, and determine properties of key sampling distributions such as the mean, proportion, and variance. The key points are:
- Sampling distributions describe the distribution of all possible values of a statistic from samples of a given size from a population.
- The sampling distribution of the mean is normally distributed for large samples, with mean equal to the population mean and standard deviation equal to the population standard deviation over the square root of the sample size.
- Even if the population is not normal, the Central Limit Theorem states that the sampling distribution of the mean will be approximately normal for large
This document provides an overview of sampling and sampling distributions. It begins by stating the chapter goals, which are to describe key sampling concepts like simple random samples and explain the differences between descriptive and inferential statistics. It then defines important terms like population, sample, and sampling distribution. The document explains that sampling is used instead of censuses because it is less time-consuming and costly while still providing sufficiently precise results. It also outlines the chapter, noting it will cover the sampling distributions of the sample mean, sample proportion, and sample variance. It provides examples of how to determine the properties of these sampling distributions such as their means and standard deviations. It emphasizes the central limit theorem and how large samples lead to normally distributed sampling distributions even
This document provides an overview of sampling and sampling distributions. It defines key concepts like populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains how sampling distributions are developed and their properties. Specifically, it discusses the sampling distribution of the sample mean, including how it has an expected value equal to the population mean and standard error that decreases as sample size increases. The Central Limit Theorem is also summarized, stating that as sample size increases, the sampling distribution will approach a normal distribution regardless of the shape of the original population.
This chapter discusses sampling distributions and their properties. It covers the sampling distribution of the mean and the proportion. The key points are:
- A sampling distribution describes the distribution of a statistic like the mean from random samples of a population.
- The Central Limit Theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normal.
- For the mean, the sampling distribution has a mean equal to the population mean and standard deviation that decreases as sample size increases.
- For a proportion, the sampling distribution can be approximated as normal if sample size n and np or n(1-p) are large enough.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This document section discusses estimating population means from sample data. It presents methods for constructing confidence intervals for the population mean using the sample mean and standard deviation. Whether the t-distribution or normal distribution is used depends on whether the population standard deviation is known. Examples are provided to illustrate calculating margins of error and interpreting confidence intervals. The key requirements are that the sample be randomly selected and the population be normally distributed or the sample size be greater than 30.
Sampling distributions stat ppt @ bec domsBabasab Patil
The document discusses sampling distributions and their properties. It defines sampling error and how to calculate it. It explains that the sampling distribution of the sample mean x is normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. Similarly, the sampling distribution of the sample proportion p is normally distributed when the sample size is large. The Central Limit Theorem states that the sampling distribution will be approximately normal for large sample sizes regardless of the population distribution.
This document discusses sampling distributions and their properties. It begins by describing the distribution of the sample mean for both normal and non-normal populations. As sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the population distribution. The document then discusses the sampling distribution of the sample proportion. For large samples, this distribution is approximately normal with mean equal to the population proportion and standard deviation inversely related to sample size. Examples are provided to illustrate computing sample proportions and probabilities involving sampling distributions.
This document provides an overview of confidence interval estimation. It discusses constructing confidence intervals for estimating population means and proportions. When the population standard deviation is known, confidence intervals for the mean can be constructed using a normal distribution. When the standard deviation is unknown, a t-distribution is used instead. Confidence intervals for proportions are estimated using the normal approximation to the binomial distribution. Examples are provided to demonstrate how to calculate confidence intervals.
This document provides an overview of confidence interval estimation. It discusses how confidence intervals can be constructed for estimating a population mean or proportion. When the population standard deviation is known, confidence intervals for the mean use the normal distribution. When the standard deviation is unknown, t-distributions are used instead. Examples are provided to demonstrate how to calculate confidence intervals and interpret the results. The goal of confidence intervals is to provide a range of plausible values for the unknown population parameter with a specific level of confidence, such as 95%.
usiness statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This chapter discusses additional topics in sampling, including:
- The basic steps of a sampling study and types of sampling errors
- Methods such as simple random sampling, stratified sampling, and estimating population parameters like the mean, total, and proportion from samples
- How to determine sample sizes and construct confidence intervals for estimating population values
- Other sampling methods like cluster sampling and non-probability samples are also introduced.
The central limit theorem states that the sampling distribution of the sample mean x will be approximately normally distributed for sample sizes n greater than 30, regardless of the shape of the population distribution. Specifically, the sampling distribution of x will have a mean equal to the population mean μ and a standard deviation of σ/√n. Similarly, for a sample proportion p, the sampling distribution of p will be approximately normal for n greater than 10 and np and nq both greater than 10, with mean equal to the population proportion p and standard deviation of √(p(1-p)/n).
This chapter discusses the fundamentals of hypothesis testing, including:
- The basic process involves stating a null hypothesis, collecting sample data, calculating a test statistic, and determining whether to reject or fail to reject the null hypothesis based on critical values.
- Type I and Type II errors can occur depending on whether the null hypothesis is true or false and the decision that is made. Researchers aim to control the level of Type I errors.
- Hypothesis tests for a mean can use a z-test if the population standard deviation is known, or a t-test if it is unknown. The p-value approach compares the calculated p-value to the significance level to determine whether to reject the null hypothesis.
This document provides an overview of simple linear regression. It begins with introducing probabilistic models and the general form of a first-order probabilistic model. It then discusses fitting a simple linear regression model to data using the least squares approach to estimate the parameters β0 and β1. It also covers the assumptions of the regression model and how to assess the utility of the model, including testing whether the slope coefficient β1 is statistically significant. An example is provided to illustrate these concepts.
InstructionDue Date 6 pm on October 28 (Wed)Part IProbability a.docxdirkrplav
This document discusses implementing a social, environmental, and economic impact measurement system within a company. It explains that measuring sustainability performance is critical for evaluating projects, the company, and its members. A proper measurement system allows companies to develop a sustainability strategy, allocate resources to support it, and evaluate trade-offs between sustainability projects. The document provides examples from Nike and P&G of measuring impacts to demonstrate the business case for sustainability. It stresses that measurement is important for linking performance to sustainability principles and facilitating continuous improvement.
This chapter discusses sampling and sampling distributions. It defines key sampling concepts like the sampling frame, population, and different sampling methods including probability and non-probability samples. Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. The chapter also covers sampling distributions and how the distribution of sample means approaches a normal distribution as the sample size increases due to the Central Limit Theorem, even if the population is not normally distributed. This allows inferring properties of the population from a sample.
This chapter discusses additional topics related to estimation, including forming confidence intervals for differences between dependent and independent population means and proportions. It provides formulas and examples for confidence intervals when population variances are known or unknown, and when variances are assumed equal or unequal. The chapter goals are to enable readers to compute confidence intervals and determine sample sizes for a variety of estimation problems involving means, proportions, differences between populations, and variances.
This chapter discusses numerical descriptive measures used to describe data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation, coefficient of variation), and shape. It provides definitions and formulas for calculating these measures, as well as examples of interpreting and comparing them. The mean is the most common measure of central tendency, while the standard deviation is generally the best measure of variation. Measures of central tendency and variation are useful for summarizing and understanding the key properties of numerical data.
Chapter 5 part2- Sampling Distributions for Counts and Proportions (Binomial ...nszakir
Mathematics, Statistics, Sampling Distributions for Counts and Proportions, Binomial Distributions for Sample Counts,
Binomial Distributions in Statistical Sampling, Binomial Mean and Standard Deviation, Sample Proportions, Normal Approximation for Counts and Proportions, Binomial Formula
This chapter discusses additional sampling methods including stratified sampling, cluster sampling, and two-phase sampling. It provides formulas for estimating population means, totals, and proportions from stratified and cluster samples. Methods for determining optimal sample sizes to achieve desired levels of precision are also presented. Finally, the chapter addresses non-probability sampling techniques and their limitations compared to probability samples.
This document contains sections from a textbook on elementary statistics and the central limit theorem. It provides an explanation of the central limit theorem, which states that the distribution of sample means approaches the normal distribution as sample size increases, regardless of the population distribution. It also contains examples demonstrating how the distribution of means becomes more normal for different population distributions as the sample size grows. Finally, it includes an example problem applying the central limit theorem to calculate the probability that the total weight of 16 male passengers exceeds the maximum capacity of an elevator.
law of large number and central limit theoremlovemucheca
The document provides information about the Law of Large Numbers and the Central Limit Theorem. It discusses two key concepts:
1) As the sample size increases, the sample average converges to the population average. This is known as the Law of Large Numbers and "guarantees" stable long-term results for random events.
2) Regardless of the underlying population distribution, as sample size increases, the sample mean will be approximately normally distributed around the population mean. This is the Central Limit Theorem, which allows sample means and proportions to be analyzed using normal probability models.
The document provides examples to illustrate how these concepts can be applied, such as using the Central Limit Theorem to determine the probability that a sample average
Strategic management is the ongoing planning, monitoring, analysis and assessment of all necessities an organization needs to meet its goals and objectives. Changes in business environments will require organizations to constantly assess their strategies for success. The strategic management process helps organizations take stock of their present situation, chalk out strategies, deploy them and analyze the effectiveness of the implemented management strategies. Strategic management strategies consist of five basic strategies and can differ in implementation depending on the surrounding environment. Strategic management applies both to on-premise and mobile platforms.
Chapter 1 Introduction to Strategic Management.pptnajwalyaa
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This document section discusses estimating population means from sample data. It presents methods for constructing confidence intervals for the population mean using the sample mean and standard deviation. Whether the t-distribution or normal distribution is used depends on whether the population standard deviation is known. Examples are provided to illustrate calculating margins of error and interpreting confidence intervals. The key requirements are that the sample be randomly selected and the population be normally distributed or the sample size be greater than 30.
Sampling distributions stat ppt @ bec domsBabasab Patil
The document discusses sampling distributions and their properties. It defines sampling error and how to calculate it. It explains that the sampling distribution of the sample mean x is normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. Similarly, the sampling distribution of the sample proportion p is normally distributed when the sample size is large. The Central Limit Theorem states that the sampling distribution will be approximately normal for large sample sizes regardless of the population distribution.
This document discusses sampling distributions and their properties. It begins by describing the distribution of the sample mean for both normal and non-normal populations. As sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the population distribution. The document then discusses the sampling distribution of the sample proportion. For large samples, this distribution is approximately normal with mean equal to the population proportion and standard deviation inversely related to sample size. Examples are provided to illustrate computing sample proportions and probabilities involving sampling distributions.
This document provides an overview of confidence interval estimation. It discusses constructing confidence intervals for estimating population means and proportions. When the population standard deviation is known, confidence intervals for the mean can be constructed using a normal distribution. When the standard deviation is unknown, a t-distribution is used instead. Confidence intervals for proportions are estimated using the normal approximation to the binomial distribution. Examples are provided to demonstrate how to calculate confidence intervals.
This document provides an overview of confidence interval estimation. It discusses how confidence intervals can be constructed for estimating a population mean or proportion. When the population standard deviation is known, confidence intervals for the mean use the normal distribution. When the standard deviation is unknown, t-distributions are used instead. Examples are provided to demonstrate how to calculate confidence intervals and interpret the results. The goal of confidence intervals is to provide a range of plausible values for the unknown population parameter with a specific level of confidence, such as 95%.
usiness statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This chapter discusses additional topics in sampling, including:
- The basic steps of a sampling study and types of sampling errors
- Methods such as simple random sampling, stratified sampling, and estimating population parameters like the mean, total, and proportion from samples
- How to determine sample sizes and construct confidence intervals for estimating population values
- Other sampling methods like cluster sampling and non-probability samples are also introduced.
The central limit theorem states that the sampling distribution of the sample mean x will be approximately normally distributed for sample sizes n greater than 30, regardless of the shape of the population distribution. Specifically, the sampling distribution of x will have a mean equal to the population mean μ and a standard deviation of σ/√n. Similarly, for a sample proportion p, the sampling distribution of p will be approximately normal for n greater than 10 and np and nq both greater than 10, with mean equal to the population proportion p and standard deviation of √(p(1-p)/n).
This chapter discusses the fundamentals of hypothesis testing, including:
- The basic process involves stating a null hypothesis, collecting sample data, calculating a test statistic, and determining whether to reject or fail to reject the null hypothesis based on critical values.
- Type I and Type II errors can occur depending on whether the null hypothesis is true or false and the decision that is made. Researchers aim to control the level of Type I errors.
- Hypothesis tests for a mean can use a z-test if the population standard deviation is known, or a t-test if it is unknown. The p-value approach compares the calculated p-value to the significance level to determine whether to reject the null hypothesis.
This document provides an overview of simple linear regression. It begins with introducing probabilistic models and the general form of a first-order probabilistic model. It then discusses fitting a simple linear regression model to data using the least squares approach to estimate the parameters β0 and β1. It also covers the assumptions of the regression model and how to assess the utility of the model, including testing whether the slope coefficient β1 is statistically significant. An example is provided to illustrate these concepts.
InstructionDue Date 6 pm on October 28 (Wed)Part IProbability a.docxdirkrplav
This document discusses implementing a social, environmental, and economic impact measurement system within a company. It explains that measuring sustainability performance is critical for evaluating projects, the company, and its members. A proper measurement system allows companies to develop a sustainability strategy, allocate resources to support it, and evaluate trade-offs between sustainability projects. The document provides examples from Nike and P&G of measuring impacts to demonstrate the business case for sustainability. It stresses that measurement is important for linking performance to sustainability principles and facilitating continuous improvement.
This chapter discusses sampling and sampling distributions. It defines key sampling concepts like the sampling frame, population, and different sampling methods including probability and non-probability samples. Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. The chapter also covers sampling distributions and how the distribution of sample means approaches a normal distribution as the sample size increases due to the Central Limit Theorem, even if the population is not normally distributed. This allows inferring properties of the population from a sample.
This chapter discusses additional topics related to estimation, including forming confidence intervals for differences between dependent and independent population means and proportions. It provides formulas and examples for confidence intervals when population variances are known or unknown, and when variances are assumed equal or unequal. The chapter goals are to enable readers to compute confidence intervals and determine sample sizes for a variety of estimation problems involving means, proportions, differences between populations, and variances.
This chapter discusses numerical descriptive measures used to describe data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation, coefficient of variation), and shape. It provides definitions and formulas for calculating these measures, as well as examples of interpreting and comparing them. The mean is the most common measure of central tendency, while the standard deviation is generally the best measure of variation. Measures of central tendency and variation are useful for summarizing and understanding the key properties of numerical data.
Chapter 5 part2- Sampling Distributions for Counts and Proportions (Binomial ...nszakir
Mathematics, Statistics, Sampling Distributions for Counts and Proportions, Binomial Distributions for Sample Counts,
Binomial Distributions in Statistical Sampling, Binomial Mean and Standard Deviation, Sample Proportions, Normal Approximation for Counts and Proportions, Binomial Formula
This chapter discusses additional sampling methods including stratified sampling, cluster sampling, and two-phase sampling. It provides formulas for estimating population means, totals, and proportions from stratified and cluster samples. Methods for determining optimal sample sizes to achieve desired levels of precision are also presented. Finally, the chapter addresses non-probability sampling techniques and their limitations compared to probability samples.
This document contains sections from a textbook on elementary statistics and the central limit theorem. It provides an explanation of the central limit theorem, which states that the distribution of sample means approaches the normal distribution as sample size increases, regardless of the population distribution. It also contains examples demonstrating how the distribution of means becomes more normal for different population distributions as the sample size grows. Finally, it includes an example problem applying the central limit theorem to calculate the probability that the total weight of 16 male passengers exceeds the maximum capacity of an elevator.
law of large number and central limit theoremlovemucheca
The document provides information about the Law of Large Numbers and the Central Limit Theorem. It discusses two key concepts:
1) As the sample size increases, the sample average converges to the population average. This is known as the Law of Large Numbers and "guarantees" stable long-term results for random events.
2) Regardless of the underlying population distribution, as sample size increases, the sample mean will be approximately normally distributed around the population mean. This is the Central Limit Theorem, which allows sample means and proportions to be analyzed using normal probability models.
The document provides examples to illustrate how these concepts can be applied, such as using the Central Limit Theorem to determine the probability that a sample average
Strategic management is the ongoing planning, monitoring, analysis and assessment of all necessities an organization needs to meet its goals and objectives. Changes in business environments will require organizations to constantly assess their strategies for success. The strategic management process helps organizations take stock of their present situation, chalk out strategies, deploy them and analyze the effectiveness of the implemented management strategies. Strategic management strategies consist of five basic strategies and can differ in implementation depending on the surrounding environment. Strategic management applies both to on-premise and mobile platforms.
Chapter 1 Introduction to Strategic Management.pptnajwalyaa
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This document provides an overview of a statistics course being taught at USIM. It introduces the instructor, Dr. Nursilah Ahmad, and outlines the course topics, textbook, assignments, and assessment. The course will cover descriptive and inferential statistics, the differences between samples and populations, and the four levels of measurement for variables. Students will complete two tests, an individual assignment, and a group assignment analyzing secondary data related to economics and COVID-19. The goals are for students to understand how statistics is used and be able to distinguish between different statistical concepts and variables.
The process of describing populations and samples is called Descriptive Statistics. A population includes everyone in the area of interest. For example, every person in the United States, every dog owner in Florida, or every computer user in the world. A sample is a small piece of the whole (i.e. 1000 people in the United States, 250 Floridian dog owners, 2500 worldwide computer users). There are three main ways to describe populations and samples: central tendency, dispersion and association.
The process of describing populations and samples is called Descriptive Statistics. A population includes everyone in the area of interest. For example, every person in the United States, every dog owner in Florida, or every computer user in the world. A sample is a small piece of the whole (i.e. 1000 people in the United States, 250 Floridian dog owners, 2500 worldwide computer users). There are three main ways to describe populations and samples: central tendency, dispersion and association.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
business statistics . In this chapter, you learn:
To construct and interpret confidence interval estimates for the population mean
To determine the sample size necessary to develop a confidence interval for the population mean
A point estimate is a single number,
a confidence interval provides additional information about the variability of the estimate
Suppose confidence level = 95%
Also written (1 - ) = 0.95, (so = 0.05)
A relative frequency interpretation:
95% of all the confidence intervals that can be constructed will contain the unknown true parameter
A specific interval either will contain or will not contain the true parameter
No probability involved in a specific interval. A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
Determine a 95% confidence interval for the true mean resistance of the population.
A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
We are 95% confident that the true mean resistance is between 1.9932 and 2.4068 ohms
Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean
Interpreting this interval requires the assumption that the population you are sampling from is approximately a normal distribution (especially since n is only 25).
This condition can be checked by creating a:
Normal probability plot or
Boxplot
The required sample size can be found to reach a desired margin of error (e) with a specified level of confidence (1 - )
The margin of error is also called sampling error
the amount of imprecision in the estimate of the population parameter
the amount added and subtracted to the point estimate to form the confidence interval
Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...my Pandit
Explore the fascinating world of the Gemini Zodiac Sign. Discover the unique personality traits, key dates, and horoscope insights of Gemini individuals. Learn how their sociable, communicative nature and boundless curiosity make them the dynamic explorers of the zodiac. Dive into the duality of the Gemini sign and understand their intellectual and adventurous spirit.
Brian Fitzsimmons on the Business Strategy and Content Flywheel of Barstool S...Neil Horowitz
On episode 272 of the Digital and Social Media Sports Podcast, Neil chatted with Brian Fitzsimmons, Director of Licensing and Business Development for Barstool Sports.
What follows is a collection of snippets from the podcast. To hear the full interview and more, check out the podcast on all podcast platforms and at www.dsmsports.net
At Techbox Square, in Singapore, we're not just creative web designers and developers, we're the driving force behind your brand identity. Contact us today.
Structural Design Process: Step-by-Step Guide for BuildingsChandresh Chudasama
The structural design process is explained: Follow our step-by-step guide to understand building design intricacies and ensure structural integrity. Learn how to build wonderful buildings with the help of our detailed information. Learn how to create structures with durability and reliability and also gain insights on ways of managing structures.
How are Lilac French Bulldogs Beauty Charming the World and Capturing Hearts....Lacey Max
“After being the most listed dog breed in the United States for 31
years in a row, the Labrador Retriever has dropped to second place
in the American Kennel Club's annual survey of the country's most
popular canines. The French Bulldog is the new top dog in the
United States as of 2022. The stylish puppy has ascended the
rankings in rapid time despite having health concerns and limited
color choices.”
Top mailing list providers in the USA.pptxJeremyPeirce1
Discover the top mailing list providers in the USA, offering targeted lists, segmentation, and analytics to optimize your marketing campaigns and drive engagement.
Taurus Zodiac Sign: Unveiling the Traits, Dates, and Horoscope Insights of th...my Pandit
Dive into the steadfast world of the Taurus Zodiac Sign. Discover the grounded, stable, and logical nature of Taurus individuals, and explore their key personality traits, important dates, and horoscope insights. Learn how the determination and patience of the Taurus sign make them the rock-steady achievers and anchors of the zodiac.
Best practices for project execution and deliveryCLIVE MINCHIN
A select set of project management best practices to keep your project on-track, on-cost and aligned to scope. Many firms have don't have the necessary skills, diligence, methods and oversight of their projects; this leads to slippage, higher costs and longer timeframes. Often firms have a history of projects that simply failed to move the needle. These best practices will help your firm avoid these pitfalls but they require fortitude to apply.
[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
This PowerPoint compilation offers a comprehensive overview of 20 leading innovation management frameworks and methodologies, selected for their broad applicability across various industries and organizational contexts. These frameworks are valuable resources for a wide range of users, including business professionals, educators, and consultants.
Each framework is presented with visually engaging diagrams and templates, ensuring the content is both informative and appealing. While this compilation is thorough, please note that the slides are intended as supplementary resources and may not be sufficient for standalone instructional purposes.
This compilation is ideal for anyone looking to enhance their understanding of innovation management and drive meaningful change within their organization. Whether you aim to improve product development processes, enhance customer experiences, or drive digital transformation, these frameworks offer valuable insights and tools to help you achieve your goals.
INCLUDED FRAMEWORKS/MODELS:
1. Stanford’s Design Thinking
2. IDEO’s Human-Centered Design
3. Strategyzer’s Business Model Innovation
4. Lean Startup Methodology
5. Agile Innovation Framework
6. Doblin’s Ten Types of Innovation
7. McKinsey’s Three Horizons of Growth
8. Customer Journey Map
9. Christensen’s Disruptive Innovation Theory
10. Blue Ocean Strategy
11. Strategyn’s Jobs-To-Be-Done (JTBD) Framework with Job Map
12. Design Sprint Framework
13. The Double Diamond
14. Lean Six Sigma DMAIC
15. TRIZ Problem-Solving Framework
16. Edward de Bono’s Six Thinking Hats
17. Stage-Gate Model
18. Toyota’s Six Steps of Kaizen
19. Microsoft’s Digital Transformation Framework
20. Design for Six Sigma (DFSS)
To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations
Zodiac Signs and Food Preferences_ What Your Sign Says About Your Tastemy Pandit
Know what your zodiac sign says about your taste in food! Explore how the 12 zodiac signs influence your culinary preferences with insights from MyPandit. Dive into astrology and flavors!
Industrial Tech SW: Category Renewal and CreationChristian Dahlen
Every industrial revolution has created a new set of categories and a new set of players.
Multiple new technologies have emerged, but Samsara and C3.ai are only two companies which have gone public so far.
Manufacturing startups constitute the largest pipeline share of unicorns and IPO candidates in the SF Bay Area, and software startups dominate in Germany.
[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
This presentation is a curated compilation of PowerPoint diagrams and templates designed to illustrate 20 different digital transformation frameworks and models. These frameworks are based on recent industry trends and best practices, ensuring that the content remains relevant and up-to-date.
Key highlights include Microsoft's Digital Transformation Framework, which focuses on driving innovation and efficiency, and McKinsey's Ten Guiding Principles, which provide strategic insights for successful digital transformation. Additionally, Forrester's framework emphasizes enhancing customer experiences and modernizing IT infrastructure, while IDC's MaturityScape helps assess and develop organizational digital maturity. MIT's framework explores cutting-edge strategies for achieving digital success.
These materials are perfect for enhancing your business or classroom presentations, offering visual aids to supplement your insights. Please note that while comprehensive, these slides are intended as supplementary resources and may not be complete for standalone instructional purposes.
Frameworks/Models included:
Microsoft’s Digital Transformation Framework
McKinsey’s Ten Guiding Principles of Digital Transformation
Forrester’s Digital Transformation Framework
IDC’s Digital Transformation MaturityScape
MIT’s Digital Transformation Framework
Gartner’s Digital Transformation Framework
Accenture’s Digital Strategy & Enterprise Frameworks
Deloitte’s Digital Industrial Transformation Framework
Capgemini’s Digital Transformation Framework
PwC’s Digital Transformation Framework
Cisco’s Digital Transformation Framework
Cognizant’s Digital Transformation Framework
DXC Technology’s Digital Transformation Framework
The BCG Strategy Palette
McKinsey’s Digital Transformation Framework
Digital Transformation Compass
Four Levels of Digital Maturity
Design Thinking Framework
Business Model Canvas
Customer Journey Map
Building Your Employer Brand with Social MediaLuanWise
Presented at The Global HR Summit, 6th June 2024
In this keynote, Luan Wise will provide invaluable insights to elevate your employer brand on social media platforms including LinkedIn, Facebook, Instagram, X (formerly Twitter) and TikTok. You'll learn how compelling content can authentically showcase your company culture, values, and employee experiences to support your talent acquisition and retention objectives. Additionally, you'll understand the power of employee advocacy to amplify reach and engagement – helping to position your organization as an employer of choice in today's competitive talent landscape.
Discover timeless style with the 2022 Vintage Roman Numerals Men's Ring. Crafted from premium stainless steel, this 6mm wide ring embodies elegance and durability. Perfect as a gift, it seamlessly blends classic Roman numeral detailing with modern sophistication, making it an ideal accessory for any occasion.
https://rb.gy/usj1a2
Anny Serafina Love - Letter of Recommendation by Kellen Harkins, MS.AnnySerafinaLove
This letter, written by Kellen Harkins, Course Director at Full Sail University, commends Anny Love's exemplary performance in the Video Sharing Platforms class. It highlights her dedication, willingness to challenge herself, and exceptional skills in production, editing, and marketing across various video platforms like YouTube, TikTok, and Instagram.
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HOW TO START UP A COMPANY A STEP-BY-STEP GUIDE.pdf46adnanshahzad
How to Start Up a Company: A Step-by-Step Guide Starting a company is an exciting adventure that combines creativity, strategy, and hard work. It can seem overwhelming at first, but with the right guidance, anyone can transform a great idea into a successful business. Let's dive into how to start up a company, from the initial spark of an idea to securing funding and launching your startup.
Introduction
Have you ever dreamed of turning your innovative idea into a thriving business? Starting a company involves numerous steps and decisions, but don't worry—we're here to help. Whether you're exploring how to start a startup company or wondering how to start up a small business, this guide will walk you through the process, step by step.