This chapter discusses two-sample hypothesis tests for comparing population means and proportions between two independent samples, and between two related samples. It introduces tests for comparing the means of two independent populations, two related populations, and the proportions of two independent populations. The key tests covered are the pooled variance t-test for independent samples with equal variances, separate variance t-test for independent samples with unequal variances, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct hypothesis tests to compare sample means and determine if they are statistically different. Confidence intervals for the difference between two means are also discussed.
This chapter discusses analysis of variance (ANOVA) techniques. It covers one-way and two-way ANOVA for comparing the means of three or more groups or populations. The chapter explains how to partition total variation into between-group and within-group components using sum of squares calculations. It also describes how to conduct the F-test and make inferences about differences in population means using ANOVA tables and significance tests. Multiple comparison procedures for identifying specific mean differences are also introduced.
This chapter discusses confidence interval estimation for means and proportions. It introduces key concepts such as point estimates, confidence intervals, and confidence levels. For a mean where the population standard deviation is known, the confidence interval formula uses the normal distribution. When the standard deviation is unknown, the t-distribution is used instead. For a proportion, the confidence interval adds an allowance for uncertainty to the sample proportion. The chapter also covers determining sample sizes and interpreting confidence intervals.
This document provides an overview of simple linear regression analysis. It defines key concepts such as the regression line, slope, intercept, and correlation coefficient. It also explains how to evaluate the fit of a regression model using the coefficient of determination (R2), which measures the proportion of variance in the dependent variable that is explained by the independent variable. The document includes an example using house price and square footage data to demonstrate how to apply simple linear regression and interpret the results.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
This chapter discusses confidence interval estimation. It covers constructing confidence intervals for a single population mean when the population standard deviation is known or unknown, as well as confidence intervals for a single population proportion. The chapter defines key concepts like point estimates, confidence levels, and degrees of freedom. It provides examples of how to calculate confidence intervals using the normal, t, and binomial distributions and how to interpret the resulting intervals.
This document discusses the normal distribution and other continuous probability distributions. It begins by listing the learning objectives, which are to compute probabilities from the normal, uniform, exponential, and binomial distributions. It then defines continuous random variables and describes key properties of the normal distribution, including its bell shape, equal mean, median and mode, and symmetry. Several examples are provided to illustrate how to compute probabilities using the normal distribution and standardized normal table. The empirical rules for the normal distribution are also discussed.
This chapter discusses chi-square tests and nonparametric tests. It covers chi-square tests for contingency tables to test differences between two or more proportions, including computing expected frequencies. The Marascuilo procedure is introduced for determining pairwise differences when proportions are found to be unequal. Chi-square tests of independence are discussed for contingency tables with more than two variables to test if the variables are independent. Nonparametric tests are also introduced. Examples are provided to demonstrate chi-square goodness of fit tests and tests of independence.
This chapter discusses confidence interval estimation. It defines point estimates and confidence intervals, and explains how to construct confidence intervals for a population mean when the population standard deviation is known or unknown, as well as for a population proportion. When the population standard deviation is unknown, a t-distribution rather than normal distribution is used. Formulas and examples are provided. The chapter also addresses determining the required sample size to estimate a mean or proportion within a specified margin of error.
This chapter discusses analysis of variance (ANOVA) techniques. It covers one-way and two-way ANOVA for comparing the means of three or more groups or populations. The chapter explains how to partition total variation into between-group and within-group components using sum of squares calculations. It also describes how to conduct the F-test and make inferences about differences in population means using ANOVA tables and significance tests. Multiple comparison procedures for identifying specific mean differences are also introduced.
This chapter discusses confidence interval estimation for means and proportions. It introduces key concepts such as point estimates, confidence intervals, and confidence levels. For a mean where the population standard deviation is known, the confidence interval formula uses the normal distribution. When the standard deviation is unknown, the t-distribution is used instead. For a proportion, the confidence interval adds an allowance for uncertainty to the sample proportion. The chapter also covers determining sample sizes and interpreting confidence intervals.
This document provides an overview of simple linear regression analysis. It defines key concepts such as the regression line, slope, intercept, and correlation coefficient. It also explains how to evaluate the fit of a regression model using the coefficient of determination (R2), which measures the proportion of variance in the dependent variable that is explained by the independent variable. The document includes an example using house price and square footage data to demonstrate how to apply simple linear regression and interpret the results.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
This chapter discusses confidence interval estimation. It covers constructing confidence intervals for a single population mean when the population standard deviation is known or unknown, as well as confidence intervals for a single population proportion. The chapter defines key concepts like point estimates, confidence levels, and degrees of freedom. It provides examples of how to calculate confidence intervals using the normal, t, and binomial distributions and how to interpret the resulting intervals.
This document discusses the normal distribution and other continuous probability distributions. It begins by listing the learning objectives, which are to compute probabilities from the normal, uniform, exponential, and binomial distributions. It then defines continuous random variables and describes key properties of the normal distribution, including its bell shape, equal mean, median and mode, and symmetry. Several examples are provided to illustrate how to compute probabilities using the normal distribution and standardized normal table. The empirical rules for the normal distribution are also discussed.
This chapter discusses chi-square tests and nonparametric tests. It covers chi-square tests for contingency tables to test differences between two or more proportions, including computing expected frequencies. The Marascuilo procedure is introduced for determining pairwise differences when proportions are found to be unequal. Chi-square tests of independence are discussed for contingency tables with more than two variables to test if the variables are independent. Nonparametric tests are also introduced. Examples are provided to demonstrate chi-square goodness of fit tests and tests of independence.
This chapter discusses confidence interval estimation. It defines point estimates and confidence intervals, and explains how to construct confidence intervals for a population mean when the population standard deviation is known or unknown, as well as for a population proportion. When the population standard deviation is unknown, a t-distribution rather than normal distribution is used. Formulas and examples are provided. The chapter also addresses determining the required sample size to estimate a mean or proportion within a specified margin of error.
The Normal Distribution and Other Continuous DistributionsYesica Adicondro
The document describes concepts related to the normal distribution and other continuous probability distributions. It introduces the normal distribution and its properties including that it is bell-shaped and symmetric with the mean, median and mode being equal. It describes how the mean and standard deviation determine the location and spread of the distribution. It also covers translating problems to the standardized normal distribution and how to find probabilities using the normal distribution table and by calculating the area under the normal curve.
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
Chapter Topic:
Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
Potential Hypothesis-Testing Pitfalls and Ethical Issues
This chapter discusses numerical descriptive measures used to describe the central tendency, variation, and shape of data. It covers calculating the mean, median, mode, variance, standard deviation, and coefficient of variation for data. The geometric mean is introduced as a measure of the average rate of change over time. Outliers are identified using z-scores. Methods for summarizing and comparing data using these descriptive statistics are presented.
This chapter discusses hypothesis testing for comparing means and variances between two populations or samples. It covers testing for the difference between two independent population means, two related (paired) population means, and two independent population variances. The key tests covered are the pooled variance t-test and separate variance t-test for independent samples, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct the hypothesis test to determine if the means or variances are significantly different.
This document discusses one-sample hypothesis tests. It defines key terms like hypotheses, null and alternative hypotheses, Type I and Type II errors, test statistics, critical values, one-tailed and two-tailed tests. It provides examples of how to set up and conduct hypothesis tests to analyze a population mean. This includes situations when the population standard deviation is known or unknown. The examples show how to state the hypotheses, select the significance level, identify the appropriate test statistic, determine the decision rule, and make a conclusion.
This chapter discusses various methods for organizing and presenting data through tables and graphs. It covers techniques for categorical data like summary tables, bar charts, pie charts and Pareto diagrams. For numerical data, it discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, frequency polygons and ogives. It also introduces methods for presenting multivariate categorical data using contingency tables and side-by-side bar charts. The goal is to choose the most effective way to summarize and communicate patterns in the data.
This document discusses key concepts in research methods and biostatistics, including hypothesis testing, random error, p-values, and confidence intervals. It explains that hypothesis testing involves determining if study findings reflect chance or a true effect. The p-value represents the probability of observing results as extreme or more extreme than what was observed by chance alone. A p-value less than 0.05 indicates statistical significance. Confidence intervals provide a range of values that are likely to contain the true population parameter.
This chapter introduces basic probability concepts including sample spaces, events, simple probability, joint probability, and conditional probability. It defines key terms and provides examples of calculating probabilities using contingency tables and decision trees. Probability rules are examined, including the general addition rule and rules for mutually exclusive and collectively exhaustive events. The chapter also covers statistical independence, marginal probability, and Bayes' theorem for calculating conditional probabilities.
This chapter discusses basic probability concepts, including defining probability, sample spaces, simple and joint events, and assessing probability through classical and subjective approaches. It also covers key probability rules like the general addition rule, computing conditional probabilities, statistical independence, and Bayes' theorem. The goals are to explain these fundamental probability topics, show how to apply common probability rules, and determine if events are statistically independent or dependent.
Basic statistics is the science of collecting, organizing, summarizing, and interpreting data. It allows researchers to gain insights from data through graphical or numerical summaries, regardless of the amount of data. Descriptive statistics can be used to describe single variables through frequencies, percentages, means, and standard deviations. Inferential statistics make inferences about phenomena through hypothesis testing, correlations, and predicting relationships between variables.
This chapter discusses various methods for summarizing and exploring data, including dot plots, stem-and-leaf displays, percentiles, box plots, and scatter plots. Dot plots and stem-and-leaf displays organize data in a way that shows the distribution while maintaining each data point. Percentiles such as the median and quartiles divide data into equal portions. Box plots graphically show the center, spread, and outliers of data. Scatter plots reveal relationships between two variables, while contingency tables summarize categorical data relationships.
The document discusses independent and dependent events. Independent events are those where the occurrence of one event does not affect the other event, such as flipping a coin or rolling a die. Dependent events are those where one event affects the other, like drawing cards from a deck without replacement. The probability of dependent events decreases as the sample space decreases with each subsequent event, while independent events have an unchanged sample space and probability.
This document provides an overview of ordinal logistic regression (OLR). OLR is used when the dependent variable has ordered categories and the proportional odds assumption is met. Violations of this assumption indicate multinomial logistic regression may be a better alternative. The document discusses key aspects of OLR including interpretation of regression coefficients and odds ratios. It also provides an example analyzing predictors of student interest, finding mastery goals and passing a previous test significantly increased odds of higher interest while fear of failure decreased odds.
This chapter discusses important discrete probability distributions used in business statistics. It introduces discrete random variables and their probability distributions. It defines the binomial distribution and explains how to calculate probabilities using the binomial formula. Examples are provided to demonstrate calculating the mean, variance, and covariance of discrete random variables, as well as the expected value and risk of investment portfolios. Counting techniques like combinations are also discussed for calculating binomial probabilities.
This document provides an overview of point estimation methods, including maximum likelihood estimation and the method of moments. It begins with an introduction to statistical inference and the theory of estimation. Point estimation is defined as using sample data to calculate a single value as the best estimate of an unknown population parameter. Maximum likelihood estimation maximizes the likelihood function to find the parameter values that make the observed sample data most probable. The method of moments equates sample moments to theoretical moments to derive parameter estimates. Examples are provided to illustrate how to apply each method to obtain point estimators.
The document provides an overview of analysis of variance (ANOVA) techniques, including:
- One-way ANOVA to evaluate differences between three or more group means and the assumptions of one-way ANOVA.
- Partitioning total variation into between-group and within-group components.
- Computing test statistics like the F-ratio to test for differences between group means.
- Interpreting one-way ANOVA results including rejecting the null hypothesis of no difference between means.
- An example one-way ANOVA calculation and interpretation using golf club distance data.
1. The document discusses different types of probability distributions including discrete, continuous, binomial, Poisson, and normal distributions.
2. It provides examples of how to calculate probabilities and expected values for each distribution using concepts like probability density functions, mean, standard deviation, and combinations.
3. Key differences between distributions are highlighted such as discrete probabilities being determined by areas under a curve for continuous distributions and Poisson distribution approximating binomial for large numbers of trials.
This document outlines key concepts related to constructing confidence intervals for estimating population means and proportions. It discusses how to calculate confidence intervals when the population standard deviation is known or unknown. Specifically, it provides the formulas and assumptions for constructing confidence intervals for a population mean using the normal and t-distributions. It also outlines how to calculate confidence intervals for a population proportion using the normal approximation. Examples are provided to demonstrate how to construct 95% confidence intervals for a mean and proportion based on sample data.
This document provides an overview of basic probability concepts covered in Chapter 4 of Basic Business Statistics, 11th Edition. It introduces key probability terms like simple events, joint events, sample space, and contingency tables for visualizing events. It covers how to calculate probabilities of events both with and without conditional dependencies. Formulas are provided for computing joint, marginal, and conditional probabilities using contingency tables. The chapter also explains Bayes' Theorem for revising probabilities based on new information. An example demonstrates how to apply Bayes' Theorem to calculate the probability of a successful oil well given a positive test result.
This document outlines the key goals and concepts covered in Chapter 6 of the textbook "Statistics for Managers Using Microsoft Excel". The chapter introduces continuous probability distributions, including the normal, uniform, and exponential distributions. It describes the characteristics of the normal distribution and how to translate problems into standardized normal distribution problems. The chapter also covers sampling distributions, the central limit theorem, and how to find probabilities using the normal distribution table.
This chapter discusses hypothesis testing for the difference between two population means and two population proportions. It covers tests for:
1) Matched or dependent pairs, using a t-test and assuming normal distributions.
2) Independent populations when variances are known, using a z-test.
3) Independent populations when variances are unknown but assumed equal, using a pooled variance t-test.
4) Independent populations when variances are unknown and assumed unequal, requiring other techniques.
The document provides examples and decision rules for conducting hypothesis tests on differences between two means or proportions in various situations. Formulas for calculating test statistics like z-scores and t-statistics are presented.
This chapter discusses hypothesis testing for differences between population means and variances. It covers tests for differences between two related population means using matched pairs, differences between two independent population means when variances are known and unknown, and tests of differences between two population variances. The key test statistics are t-tests and z-tests, and the chapter presents the assumptions, test statistics, and decision rules for each hypothesis test.
The Normal Distribution and Other Continuous DistributionsYesica Adicondro
The document describes concepts related to the normal distribution and other continuous probability distributions. It introduces the normal distribution and its properties including that it is bell-shaped and symmetric with the mean, median and mode being equal. It describes how the mean and standard deviation determine the location and spread of the distribution. It also covers translating problems to the standardized normal distribution and how to find probabilities using the normal distribution table and by calculating the area under the normal curve.
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
Chapter Topic:
Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
Potential Hypothesis-Testing Pitfalls and Ethical Issues
This chapter discusses numerical descriptive measures used to describe the central tendency, variation, and shape of data. It covers calculating the mean, median, mode, variance, standard deviation, and coefficient of variation for data. The geometric mean is introduced as a measure of the average rate of change over time. Outliers are identified using z-scores. Methods for summarizing and comparing data using these descriptive statistics are presented.
This chapter discusses hypothesis testing for comparing means and variances between two populations or samples. It covers testing for the difference between two independent population means, two related (paired) population means, and two independent population variances. The key tests covered are the pooled variance t-test and separate variance t-test for independent samples, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct the hypothesis test to determine if the means or variances are significantly different.
This document discusses one-sample hypothesis tests. It defines key terms like hypotheses, null and alternative hypotheses, Type I and Type II errors, test statistics, critical values, one-tailed and two-tailed tests. It provides examples of how to set up and conduct hypothesis tests to analyze a population mean. This includes situations when the population standard deviation is known or unknown. The examples show how to state the hypotheses, select the significance level, identify the appropriate test statistic, determine the decision rule, and make a conclusion.
This chapter discusses various methods for organizing and presenting data through tables and graphs. It covers techniques for categorical data like summary tables, bar charts, pie charts and Pareto diagrams. For numerical data, it discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, frequency polygons and ogives. It also introduces methods for presenting multivariate categorical data using contingency tables and side-by-side bar charts. The goal is to choose the most effective way to summarize and communicate patterns in the data.
This document discusses key concepts in research methods and biostatistics, including hypothesis testing, random error, p-values, and confidence intervals. It explains that hypothesis testing involves determining if study findings reflect chance or a true effect. The p-value represents the probability of observing results as extreme or more extreme than what was observed by chance alone. A p-value less than 0.05 indicates statistical significance. Confidence intervals provide a range of values that are likely to contain the true population parameter.
This chapter introduces basic probability concepts including sample spaces, events, simple probability, joint probability, and conditional probability. It defines key terms and provides examples of calculating probabilities using contingency tables and decision trees. Probability rules are examined, including the general addition rule and rules for mutually exclusive and collectively exhaustive events. The chapter also covers statistical independence, marginal probability, and Bayes' theorem for calculating conditional probabilities.
This chapter discusses basic probability concepts, including defining probability, sample spaces, simple and joint events, and assessing probability through classical and subjective approaches. It also covers key probability rules like the general addition rule, computing conditional probabilities, statistical independence, and Bayes' theorem. The goals are to explain these fundamental probability topics, show how to apply common probability rules, and determine if events are statistically independent or dependent.
Basic statistics is the science of collecting, organizing, summarizing, and interpreting data. It allows researchers to gain insights from data through graphical or numerical summaries, regardless of the amount of data. Descriptive statistics can be used to describe single variables through frequencies, percentages, means, and standard deviations. Inferential statistics make inferences about phenomena through hypothesis testing, correlations, and predicting relationships between variables.
This chapter discusses various methods for summarizing and exploring data, including dot plots, stem-and-leaf displays, percentiles, box plots, and scatter plots. Dot plots and stem-and-leaf displays organize data in a way that shows the distribution while maintaining each data point. Percentiles such as the median and quartiles divide data into equal portions. Box plots graphically show the center, spread, and outliers of data. Scatter plots reveal relationships between two variables, while contingency tables summarize categorical data relationships.
The document discusses independent and dependent events. Independent events are those where the occurrence of one event does not affect the other event, such as flipping a coin or rolling a die. Dependent events are those where one event affects the other, like drawing cards from a deck without replacement. The probability of dependent events decreases as the sample space decreases with each subsequent event, while independent events have an unchanged sample space and probability.
This document provides an overview of ordinal logistic regression (OLR). OLR is used when the dependent variable has ordered categories and the proportional odds assumption is met. Violations of this assumption indicate multinomial logistic regression may be a better alternative. The document discusses key aspects of OLR including interpretation of regression coefficients and odds ratios. It also provides an example analyzing predictors of student interest, finding mastery goals and passing a previous test significantly increased odds of higher interest while fear of failure decreased odds.
This chapter discusses important discrete probability distributions used in business statistics. It introduces discrete random variables and their probability distributions. It defines the binomial distribution and explains how to calculate probabilities using the binomial formula. Examples are provided to demonstrate calculating the mean, variance, and covariance of discrete random variables, as well as the expected value and risk of investment portfolios. Counting techniques like combinations are also discussed for calculating binomial probabilities.
This document provides an overview of point estimation methods, including maximum likelihood estimation and the method of moments. It begins with an introduction to statistical inference and the theory of estimation. Point estimation is defined as using sample data to calculate a single value as the best estimate of an unknown population parameter. Maximum likelihood estimation maximizes the likelihood function to find the parameter values that make the observed sample data most probable. The method of moments equates sample moments to theoretical moments to derive parameter estimates. Examples are provided to illustrate how to apply each method to obtain point estimators.
The document provides an overview of analysis of variance (ANOVA) techniques, including:
- One-way ANOVA to evaluate differences between three or more group means and the assumptions of one-way ANOVA.
- Partitioning total variation into between-group and within-group components.
- Computing test statistics like the F-ratio to test for differences between group means.
- Interpreting one-way ANOVA results including rejecting the null hypothesis of no difference between means.
- An example one-way ANOVA calculation and interpretation using golf club distance data.
1. The document discusses different types of probability distributions including discrete, continuous, binomial, Poisson, and normal distributions.
2. It provides examples of how to calculate probabilities and expected values for each distribution using concepts like probability density functions, mean, standard deviation, and combinations.
3. Key differences between distributions are highlighted such as discrete probabilities being determined by areas under a curve for continuous distributions and Poisson distribution approximating binomial for large numbers of trials.
This document outlines key concepts related to constructing confidence intervals for estimating population means and proportions. It discusses how to calculate confidence intervals when the population standard deviation is known or unknown. Specifically, it provides the formulas and assumptions for constructing confidence intervals for a population mean using the normal and t-distributions. It also outlines how to calculate confidence intervals for a population proportion using the normal approximation. Examples are provided to demonstrate how to construct 95% confidence intervals for a mean and proportion based on sample data.
This document provides an overview of basic probability concepts covered in Chapter 4 of Basic Business Statistics, 11th Edition. It introduces key probability terms like simple events, joint events, sample space, and contingency tables for visualizing events. It covers how to calculate probabilities of events both with and without conditional dependencies. Formulas are provided for computing joint, marginal, and conditional probabilities using contingency tables. The chapter also explains Bayes' Theorem for revising probabilities based on new information. An example demonstrates how to apply Bayes' Theorem to calculate the probability of a successful oil well given a positive test result.
This document outlines the key goals and concepts covered in Chapter 6 of the textbook "Statistics for Managers Using Microsoft Excel". The chapter introduces continuous probability distributions, including the normal, uniform, and exponential distributions. It describes the characteristics of the normal distribution and how to translate problems into standardized normal distribution problems. The chapter also covers sampling distributions, the central limit theorem, and how to find probabilities using the normal distribution table.
This chapter discusses hypothesis testing for the difference between two population means and two population proportions. It covers tests for:
1) Matched or dependent pairs, using a t-test and assuming normal distributions.
2) Independent populations when variances are known, using a z-test.
3) Independent populations when variances are unknown but assumed equal, using a pooled variance t-test.
4) Independent populations when variances are unknown and assumed unequal, requiring other techniques.
The document provides examples and decision rules for conducting hypothesis tests on differences between two means or proportions in various situations. Formulas for calculating test statistics like z-scores and t-statistics are presented.
This chapter discusses hypothesis testing for differences between population means and variances. It covers tests for differences between two related population means using matched pairs, differences between two independent population means when variances are known and unknown, and tests of differences between two population variances. The key test statistics are t-tests and z-tests, and the chapter presents the assumptions, test statistics, and decision rules for each hypothesis test.
This chapter discusses hypothesis testing for differences between population means and variances. It covers testing the difference between two related population means using matched pairs. It also covers testing the difference between two independent population means when the population variances are known, unknown but assumed equal, and unknown but assumed unequal. Decision rules for lower-tail, upper-tail, and two-tail tests are provided for each case.
This chapter discusses methods for comparing two population means or proportions using statistical tests. It covers tests for independent samples, including the z-test when population variances are known and the t-test when they are unknown. It also addresses paired or related samples using a z-test when the population difference variance is known, and a t-test when it is unknown. Examples are provided for hypotheses tests and confidence intervals for the difference between two means or proportions.
This chapter discusses two-sample tests, including tests for the difference between two independent population means, the difference between two related (paired) sample means, the difference between two population proportions, and the difference between two variances. It provides the formulas and procedures for conducting Z tests, t tests, and F tests for these comparisons in situations where the population standard deviations are both known and unknown. The goal is to test hypotheses about differences between parameters of two populations or to construct confidence intervals for these differences.
This chapter discusses methods for constructing confidence intervals for differences and comparisons between population parameters using sample data. It covers constructing confidence intervals for the difference between two independent population means when the standard deviations are known or unknown. It also addresses constructing confidence intervals when the population variances are assumed to be equal or unequal. The chapter concludes with constructing confidence intervals for the difference between two independent population proportions.
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 document discusses hypothesis testing methods for comparing two populations, including comparing two means and two proportions. It addresses using z-tests and t-tests to determine if there are statistically significant differences between sample means or proportions from two independent populations. Specific topics covered include assumptions of the tests, how to set up the null and alternative hypotheses, and examples of calculations for the z-test, t-test, and test for comparing two proportions.
This document discusses hypothesis testing for two populations. It covers testing whether two independent population means or proportions are equal using z-tests or t-tests. It also addresses testing whether the mean difference between paired observations is equal to zero using a t-test. Examples are provided for each test. The learning objectives are to understand how to perform these different types of two-sample hypothesis tests using the appropriate test statistic and test assumptions.
This document provides instructions and examples for conducting analysis of variance (ANOVA). It begins by listing learning objectives for the chapter, which include discussing ANOVA concepts, the F distribution characteristics, testing for equal variances between populations, organizing data into ANOVA tables, and conducting hypothesis tests to determine if treatment means are equal. It then provides examples of one-way and two-way ANOVA, including calculating sums of squares, F-statistics, and determining whether to reject the null hypothesis of equal means.
The document describes experimental designs and statistical tests used to analyze data from experiments with multiple groups. It discusses paired t-tests, independent t-tests, and analysis of variance (ANOVA). For ANOVA, it provides an example to calculate sum of squares for treatment (SST), sum of squares for error (SSE), and the F-statistic. The example shows applying a one-way ANOVA to compare average incomes of accounting, marketing and finance majors. It finds no significant difference between the groups. A randomized block design is then proposed to account for variability from GPA levels.
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 summarizes statistical tests for comparing two samples, including paired and independent samples t-tests, confidence intervals, and effect sizes. For paired samples from within-subject designs, a paired t-test is used to test for differences between means. For independent samples from between-subject designs, an independent samples t-test is used. Both tests calculate a t-statistic based on the mean difference and standard error. Confidence intervals and effect sizes can also be calculated for paired and independent sample designs. Examples are provided to demonstrate how to perform the statistical tests and calculations.
Week 5 HomeworkHomework #1Ms. Lisa Monnin is the budget dire.docxmelbruce90096
Week 5 Homework
Homework #1
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
Sales ($)
129
137
142
162
137
145
Audit ($)
128
98
128
140
148
110
132
At the 0.1 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?
(a)
State the decision rule. (Round your answer to 3 decimal places.)
Reject H0 if t >
(b)
Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)
Pooled variance
(c)
Compute the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(d)
State your decision about the null hypothesis.
H0 : μs ≤ μa
(e)
Estimate the p-value. (Round your answers to 3 decimal places.)
p-value
Homework #2
Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of Claiborne models:
$5.4
$4.3
$3.7
$6.7
$4.9
$5.9
$3.1
$5.2
$4.7
$3.5
5.8
4
3.1
5.6
6.9
The following is the amount ($000) earned by a sample of Klein models.
$2.5
$2.6
$3.5
$3.4
$2.8
$3.1
$4
$2.5
$2
$2.9
2.7
2.3
(1)
Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)
Degrees of freedom
(2)
State the decision rule for 0.01 significance level: H0: μLC ≤ μCK; H1: μLC > μCK. (Round your answer to 3 decimal places.)
Reject H0 if t>
(3)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(4)
Is it reasonable to conclude that Claiborne models earn more? Use the 0.01 significance level.
H0. It is to conclude that Claiborne models earn more.
Homework #3
A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.
Statistic
Men
Women
Sample mean
23.82
21.38
Population standard deviation
5.91
4.87
Sample size
34
36
At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?
(a)
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(b)
What is your decision regarding on null hypothesis?
The decision is the null hypothesis that the means are the same.
(c)
What is the p-value? (Round your answer to 4 decimal places.)
p-value
rev: 04_04_2012, 04_25_2014_QC_48145
Homework #4
Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a s.
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
This document presents an overview of statistical methods for comparing two populations. It discusses paired sample comparisons and independent sample comparisons. For paired samples, it covers the paired t-test and constructing confidence intervals. For independent samples, it explains how to test whether population means are equal using a z-test or t-test. Several examples are provided to demonstrate these techniques. The document also briefly discusses testing differences in population proportions and variances.
This document presents an overview of statistical techniques for comparing two populations. It discusses paired sample comparisons using a t-test and independent sample comparisons using a z-test. Examples are provided to demonstrate hypothesis testing to examine differences in population means and proportions. Specific topics covered include: paired t-tests, independent z-tests, testing situations for comparing two means, test statistics and examples comparing credit card charges and battery life. Templates are shown for conducting the tests in several examples.
The following calendar-year information is taken from the December.docxcherry686017
The following calendar-year information is taken from the December 31, 2011, adjusted trial balance and other records of Azalea Company.
1. Each team member is to be responsible for computing one of the following amounts. You are not to duplicate your teammates' work. Get any necessary amounts from teammates. Each member is to explain the computation to the team in preparation for reporting to class.
a. Materials used.
b. Factory overhead.
c. Total manufacturing costs.
d. Total cost of goods in process.
e. Cost of goods manufactured.
2. Check your cost of goods manufactured with the instructor. If it is correct, proceed to part (3).
3. Each team member is to be responsible for computing one of the following amounts. You are not to duplicate your teammates' work. Get any necessary amounts from teammates. Each member is to explain the computation to the team in preparation for reporting to class.
a. Net sales.
b. Cost of goods sold.
c. Gross profit.
d. Total operating expenses.
e. Net income or loss before taxes.
CALCULATE T TEST
Calculate the “t” value for independent groups for the following data using the formula provided in the attached word document. Using the raw measurement data presented, determine whether or not there exists a statistically significant difference between the salaries of female and male human resource managers using the appropriate t-test. Develop a testable hypothesis, confidence level, and degrees of freedom. Report the required “t” critical values based on the degrees of freedom. Show calculations.
Answer
The null hypothesis tested is
H0: There is no significant difference between the average salaries of female and male human resource managers. (µ1= µ2)
The alternative hypothesis is
H1: There is significant difference between the average salaries of female and male human resource managers. (µ1≠ µ2)
The test statistic used is
12
12
2
~
NN
DM
MM
tt
S
+-
-
=
Where
22
1122
1212
(1)(1)
11
2
DM
NsNs
S
NNNN
éùéù
-+-
=+
êúêú
+-
ëûëû
Here M1 = 62,200, M2 = 63,700
s1 = 9330.95, s2 = 6912.95
N1 = 10, N2 = 10 (See the excel sheet)
Then,
(
)
(
)
22
(101)9330.95(101)6912.95
11
101021010
DM
S
éù
-+-
éù
=+
êú
êú
+-
ëû
êú
ëû
= 3672.267768
Therefore test statistic,
62,20063,700
3672.267768
t
-
=
= -0.408466946
Degrees of freedom = N1 + N2 – 2 = 10 + 10 – 2 = 18
Let the significance level be 0.05.
Rejection criteria: Reject the null hypothesis, if the calculated value of t is greater than the critical value of t at 0.05 significance level.
The critical values can be obtained from the student’s t tables with 18 d.f. at 0.05 significance level.
Upper critical value = 2.1
Lower critical value = -2.1
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Conclusion: Fails to reject the null hypothesis. The sample does not provide enough evidence to support the claim that there is significant difference ...
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