Aron chpt 6 ed
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The document discusses distributions of sample means and how they relate to the population from which the samples are drawn. It states that the mean of a distribution of sample means is equal to the population mean. The variance of a distribution of sample means is equal to the population variance divided by the sample size. The distribution of sample means will be approximately normal in shape if each sample is large enough or if the population is normally distributed. It provides examples to illustrate these concepts.
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Aron chpt 6 ed revised
The document discusses distributions of sample means and how they relate to the population from which the samples are drawn. It states that the mean of a distribution of sample means is equal to the population mean. The variance of a distribution of sample means is equal to the population variance divided by the sample size. And the shape of a distribution of sample means approximates a normal distribution if each sample is at least 30 individuals or if the population is normally distributed.
Definition statistics -unknown
Statistics involves collecting, organizing, analyzing, and interpreting numerical data. Descriptive statistics describes data while inferential statistics draws conclusions from samples to populations. A study on coyotes concluded they were all dangerous based on ranchers' observations of those near ranches, but further study found most coyotes avoid sheep. Experiments aim to observe changes from treatments by comparing experimental and control groups, while observational studies make uncontrolled observations. Surveys can introduce biases from question wording, non-responses, and over-generalizing results.
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Aron chpt 6 ed revised
The document discusses distributions of sample means and how they relate to the population from which the samples are drawn. It states that the mean of a distribution of sample means is equal to the population mean. The variance of a distribution of sample means is equal to the population variance divided by the sample size. And the shape of a distribution of sample means approximates a normal distribution if each sample is at least 30 individuals or if the population is normally distributed.
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2. The sampling distribution of the standard deviation, which follows a chi-squared distribution with n-1 degrees of freedom when the population variance is σ2.
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Chapter 2 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed
Aron chpt 8 ed
The document provides an introduction to t-tests, including the t-test for a single sample and the t-test for dependent means. It explains that t-tests are used when the population variance is unknown, and compares t-tests to Z-tests. The key steps for conducting a t-test for a single sample and a t-test for dependent means are outlined. These include restating the hypotheses, determining characteristics of the comparison distribution such as the population mean and variance, finding the cutoff score, determining the sample's score, and deciding whether to reject the null hypothesis. Examples are provided to demonstrate how to perform each type of t-test.
Aron chpt 8 ed
The document provides an introduction to t-tests, including the t-test for a single sample and the t-test for dependent means. It explains that t-tests are used when the population variance is unknown, and compares t-tests to Z-tests. The key steps for conducting a t-test for a single sample and a t-test for dependent means are outlined. These include restating the hypotheses, determining characteristics of the comparison distribution such as the population mean and variance, finding the cutoff score, determining the sample's score, and deciding whether to reject the null hypothesis. Examples are provided to demonstrate how to perform each type of t-test.
Chapter one on sampling distributions.ppt
The document discusses sampling distributions and their properties. It introduces key concepts like population parameters, sample statistics, estimators, and the central limit theorem. It explains that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution with a mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. The sampling distribution tells us how close sample statistics are likely to be to the corresponding population parameters.
Chp11 - Research Methods for Business By Authors Uma Sekaran and Roger Bougie
This document discusses sampling and sampling distributions. It defines key concepts like population, sample, probability distributions, sampling distributions, and the central limit theorem. It explains that as sample size increases, the sampling distribution approximates a normal distribution according to the central limit theorem. It also discusses different types of sampling methods like simple random sampling, systematic random sampling, and stratified random sampling.
The sampling distribution
The document defines a sampling distribution of sample means as a distribution of means from random samples of a population. The mean of sample means equals the population mean, and the standard deviation of sample means is smaller than the population standard deviation, equaling it divided by the square root of the sample size. As sample size increases, the distribution of sample means approaches a normal distribution according to the Central Limit Theorem.
Sampling and sampling distributions
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Aron chpt 9 ed f2011
The document provides an overview of how to conduct a t-test for independent means. It explains that this test is used to compare the means of two independent groups and determines if any difference observed could have been due to chance. It outlines the steps for this test, including calculating the pooled variance estimate, figuring the variance of each group's distribution of means, determining the variance and standard deviation of the distribution of differences between means, and computing the t-score to compare to critical values from the t-table. An example is also provided to demonstrate how to perform a t-test for independent means on sample data.
5_lectureslides.pptx
This document provides an overview of Module 5 on sampling distributions. It discusses key concepts like parameters vs statistics, sampling variability, and sampling distributions. It explains that the sampling distribution of a sample mean is a normal distribution with a mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. The central limit theorem states that as the sample size increases, the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution. The module also covers binomial distributions for sample counts and proportions.
Chapter 11 Psrm
This document provides an overview of key concepts in descriptive statistics including measures of central tendency (mode, median, mean), measures of dispersion (range, variance, standard deviation), the normal distribution, z-scores, hypothesis testing, and the t-distribution. It defines each concept and provides examples of calculating and interpreting common statistics.
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Probability and Samples: The Distribution of Sample Means
Probability and Samples: The Distribution of Sample Means
Chp11 - Research Methods for Business By Authors Uma Sekaran and Roger Bougie
Chp11 - Research Methods for Business By Authors Uma Sekaran and Roger Bougie
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Newletter v 2.1
The newsletter welcomes over 150 new students and 20 new faculty to the ADP program at Belmont Abbey College for the fall 2012 semester. It highlights the expansion of the ADP space with the renovation of Mercedes Hall, including a new student lounge, chapel, and upcoming computer lab. It provides upcoming important dates and encourages students to get involved with tutoring services available through the Academic Resource Center.
Newletter v 2.1
The newsletter welcomes over 150 new students and 20 new faculty to the ADP program at Belmont Abbey College for the fall 2012 semester. It highlights the expansion of the Mercedes Hall building to provide more classrooms and study spaces for students. It provides upcoming dates and announces a giveaway contest for students who display an ADP decal on their cars. The student services feature promotes tutoring services available through the Academic Resource Center.
Night owl
The newsletter provides information about Bellmont Abbey College's Adult Degree Program (ADP). It highlights an upcoming basketball game on February 24th that ADP students can attend for free. It also features a student profile, the program's calendar of events including a music performance and play, and tips on nutrition, exercise and note-taking.
Simple random sample using excel
To generate a simple random sample using Excel, enter data into a sheet, click Data Analysis under the Data tab, select Sampling, highlight the input range and number of samples, click OK, and the random sample will appear in the selected output range.
Chap015
This document provides an overview of index numbers and how to compute different types of indexes. It defines an index number as a number that measures relative change from one time period to another in items like price, quantity, or value. It describes simple, unweighted indexes and weighted indexes like the Laspeyres and Paasche indexes. It provides examples of how to calculate and interpret simple indexes, Laspeyres indexes, Paasche indexes, Fisher's ideal index, and value indexes. The learning objectives cover computing and interpreting these different index types.
Chap010
This document discusses hypothesis testing and outlines the key steps in conducting hypothesis tests. It defines key terms like the null hypothesis, alternate hypothesis, Type I and Type II errors. It also distinguishes between one-tailed and two-tailed tests. Examples are provided to demonstrate how to set up and conduct hypothesis tests to analyze population means when the population standard deviation is both known and unknown. The learning objectives covered include defining hypotheses, explaining the hypothesis testing procedure, describing types of errors, using test statistics, and conducting tests on population means and proportions.
Chap009
Here are the steps to solve this problem:
1) Given: n = 10, x = 0.32, s = 0.09
2) The degrees of freedom is n - 1 = 10 - 1 = 9
3) The t-value for a 95% CI with 9 df is t0.025,9 = 2.262 (from t-table)
4) The CI is: x ± t*s/√n = 0.32 ± 2.262*(0.09/√10) = 0.32 ± 0.029
5) The 95% CI is 0.291 to 0.349 inches
6) 0.30 inches is within the CI, so it would be
Chap007
This chapter discusses several key continuous probability distributions including the uniform, normal, and exponential distributions. It covers the characteristics and formulas for computing probabilities for each distribution. For the uniform distribution, it discusses how to calculate the mean, find probabilities, and graph the distribution. For the normal distribution, it outlines the characteristics of the bell curve shape and covers converting to the standard normal distribution and using the empirical rule. It also provides examples of finding probabilities for observations within given ranges of a normal distribution.
Finding areas for z using excel
This document provides instructions for using the NORMDIST and NORMINV functions in Excel to find areas under the normal curve and find x-values given areas. For NORMDIST, the user enters values for x, mean, standard deviation and selects true for cumulative to find the area from the left of the distribution to x. For NORMINV, the user enters the probability, mean and standard deviation to find the x-value corresponding to that area. Both note that results are for the cumulative area and adjustments may be needed for the area between the mean and x.
Calculating binomial probabilities using excel
This document provides instructions for using the BINOMDIST function in Excel to calculate the probability of a certain number of successes in a fixed number of trials when the probability of success is known. Specifically, it shows how to calculate the probability that exactly 2 out of 9 individuals surveyed have used a discount broker, given that the survey found the probability of an individual investor using a discount broker to be 30%. The answer provided is that there is a 27% chance of exactly 2 of the 9 individuals having used a discount broker.
Chap008
This document provides an overview of sampling methods and the central limit theorem. It defines key learning objectives around sampling, describes common probability sampling methods like simple random sampling and stratified random sampling. It introduces the concept of sampling distribution of the sample mean and explains how the central limit theorem states that the sampling distribution of the sample mean approximates a normal distribution, even if the population is not normally distributed.
Chap006
The document discusses various probability distributions including discrete, binomial, hypergeometric, and Poisson distributions. It provides learning objectives on identifying characteristics of probability distributions, distinguishing between discrete and continuous random variables, computing means, variances and probabilities. Examples are given to illustrate computing probabilities and distributions for binomial, hypergeometric and Poisson distributions. The key characteristics, formulas, and applications of each distribution are defined.
Chap004
This document describes chapter 4 of a statistics textbook. It provides 7 learning objectives related to describing and exploring data through various statistical techniques. These include constructing and interpreting dot plots, stem-and-leaf displays, box plots, and scatterplots. It also covers measures of central tendency, percentiles, skewness, and contingency tables. Examples are provided for each statistical technique to help illustrate how to compute and interpret the various descriptive statistics.
Creating frequency distribution table, histograms and polygons using excel an...
This document provides instructions for creating frequency distribution tables, histograms, and polygons using Excel's Analysis ToolPak. It guides the user through downloading sample sales data, determining the number of classes and class intervals, setting up bins and frequency tables, and generating histograms, frequency polygons, and cumulative frequency polygons. Key steps include using formulas to calculate the number of classes and class interval size, setting up the frequency table and bins, and using Excel's Data Analysis tool and charting features to generate the graphs.
Creating frequency distribution tables and histograms using excel analysis to...
This document provides instructions for creating a frequency distribution table and histogram in Excel using the Analysis ToolPak. It explains how to determine the number of classes and class intervals using formulas. It then walks through downloading sample sales data, setting up the class intervals or "bins", generating the frequency table and histogram using the Data Analysis tool, and formatting the output properly with labels and resized charts.
Chap005
This document discusses probability concepts covered in Chapter 5. It begins by defining key terms like probability, experiment, outcome, and event. It then explains the three approaches to assigning probabilities: classical, empirical, and subjective. Next, it covers calculating probabilities using the rules of addition, multiplication, and the complement rule. It also defines joint probability and discusses calculating probabilities using Venn diagrams and contingency tables. The learning objectives cover all these essential probability topics.
Chap003
This document provides an overview of key concepts for describing numerical data, including measures of central tendency (such as the mean, median, mode, weighted mean, and geometric mean) and measures of dispersion (such as the range, mean deviation, variance and standard deviation). It defines each measure and provides examples to demonstrate how to calculate and interpret the measures. The learning objectives cover explaining the concept of central tendency, identifying and computing various measures of central tendency and dispersion, and applying the measures to analyze datasets.
Chap004
This document discusses methods for describing and exploring data including dot plots, stem-and-leaf displays, measures of position like percentiles and quartiles, and box plots. It provides examples of each method and how to interpret the results. Key learning objectives covered are constructing and interpreting dot plots, stem-and-leaf displays, computing measures of position like percentiles and quartiles, and developing and analyzing box plots from given data.
Chap002
This document discusses various methods for organizing and presenting data visually, including frequency tables, bar charts, pie charts, frequency distributions, histograms, and frequency polygons. It provides examples and learning objectives for how to create each of these and use them to summarize key characteristics of a data set such as profits from vehicle sales.
Aron chpt 1 ed (1)
Here are the steps to complete the frequency table:
9 II 2
10 0 0
Total 20 20
Copyright © 2011 by Pearson Education, Inc. All rights reserved.
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Aron chpt 6 ed
- 6. Example 2 Copyright © 2011 by Pearson Education, Inc. All rights reserved
- 7. die 1 die 2 Ave. die 1 die 2 Ave. die 1 die 2 Ave. 1 1 1 1 13 3 1 2 13 5 1 3 2 1 2 1.5 14 3 2 2.5 14 5 2 3.5 3 1 3 2 15 3 3 3 15 5 3 4 4 1 4 2.5 16 3 4 3.5 16 5 4 4.5 5 1 5 3 17 3 5 4 17 5 5 5 6 1 6 3.5 18 3 6 4.5 18 5 6 5.5 7 2 1 1.5 19 4 1 2.5 19 6 1 3.5 8 2 2 2 20 4 2 3 20 6 2 4 9 2 3 2.5 21 4 3 3.5 21 6 3 4.5 10 2 4 3 22 4 4 4 22 6 4 5 11 2 5 3.5 23 4 5 4.5 23 6 5 5.5 12 2 6 4 24 4 6 5 24 6 6 6
- 8. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1
- 9. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 72 samples mean f 1 2 1.5 4 2 6 2.5 8 3 10 3.5 12 4 10 4.5 8 5 6 5.5 4 6 2
- 10. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 108 samples mean f 1 3 1.5 6 2 9 2.5 12 3 15 3.5 18 4 15 4.5 12 5 9 5.5 6 6 3
- 11. 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 288 samples mean f 1 8 1.5 16 2 24 2.5 32 3 40 3.5 48 4 40 4.5 32 5 24 5.5 16 6 8
- 17. Standard Deviation of a Distribution of Means Copyright © 2011 by Pearson Education, Inc. All rights reserved Pop. SD = 2.5 in.
- 20. die 1 f 1 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 1 6 5 4 3 2 1 1 2 3 4 5 6
- 21. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1