Suppose a cosmetics company wants to test the effectiveness of three different sales training programs. Steve, an analyst in the company's HR department, randomly assigns 18 new employees, 6 each, to the training programs. After the training program is complete, each employee takes a product knowledge and sales skills assessment test, where scores are on a scale from 0 to 100. Steve records the assessment test results for each employee and analyzes the sample data. The distribution of test scores for each sample is approximately normal without any outliers. As population variances are unknown, Steve assumes equal variances based on the sample data because side-by-side boxplots of the samples indicate relatively equal sizes of the variances. Steve intends to conduct a one-way ANOVA ?-test at a significance level of ?=0.05 to test if the mean assessment test scores for the three training programs are all equal. The mean square between groups, MSG, is 176.1667 and the mean square within groups, also referred to as the mean square error, MSE, is 33.8444. Steve computes the ?-statistic, which is ?=5.2052. Select the statement that accurately evaluates whether or not the requirements of a one-way ANOVA ?-test have been met in Steve's experiment. If the requirements have not been met, do not proceed to answer subsequent questions. The requirements have been met because the sampling distributions are approximately normal and the dependent variable is categorical. The requirements have not been met because the sample sizes are not properly selected and are not large enough. The requirements have not been met because the population variances are unknown. The requirements have been met because the samples are properly selected, are normally distributed, and of equal sizes. The requirements have been met because the samples are properly selected and are approximately normally distributed with equal variances. If the test requirements have been met, compute the degrees of freedom for the means square between groups, MSG, and the degress of freedom for the mean square error, MSE. df1 = df2 = Determine the critical value of ? for Steve's hypothesis test at the significance level of ?=0.05 using software or an ?-distribution table. Give your answer to at least two decimal places. ?-critical value =

Suppose a cosmetics company wants to test the effectiveness of three different sales training programs. Steve, an analyst in the company's HR department, randomly assigns 18 new employees, 6 each, to the training programs. After the training program is complete, each employee takes a product knowledge and sales skills assessment test, where scores are on a scale from 0 to 100. Steve records the assessment test results for each employee and analyzes the sample data. The distribution of test scores for each sample is approximately normal without any outliers. As population variances are unknown, Steve assumes equal variances based on the sample data because side-by-side boxplots of the samples indicate relatively equal sizes of the variances. Steve intends to conduct a one-way ANOVA ?-test at a significance level of ?=0.05 to test if the mean assessment test scores for the three training programs are all equal. The mean square between groups, MSG, is 176.1667 and the mean square within groups, also referred to as the mean square error, MSE, is 33.8444. Steve computes the ?-statistic, which is ?=5.2052. Select the statement that accurately evaluates whether or not the requirements of a one-way ANOVA ?-test have been met in Steve's experiment. If the requirements have not been met, do not proceed to answer subsequent questions. The requirements have been met because the sampling distributions are approximately normal and the dependent variable is categorical. The requirements have not been met because the sample sizes are not properly selected and are not large enough. The requirements have not been met because the population variances are unknown. The requirements have been met because the samples are properly selected, are normally distributed, and of equal sizes. The requirements have been met because the samples are properly selected and are approximately normally distributed with equal variances. If the test requirements have been met, compute the degrees of freedom for the means square between groups, MSG, and the degress of freedom for the mean square error, MSE. df1 = df2 = Determine the critical value of ? for Steve's hypothesis test at the significance level of ?=0.05 using software or an ?-distribution table. Give your answer to at least two decimal places. ?-critical value =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Steve records the assessment test results for each employee and analyzes the sample data. The distribution of test scores for each sample is approximately normal without any outliers. As population variances are unknown, Steve assumes equal variances based on the sample data because side-by-side boxplots of the samples indicate relatively equal sizes of the variances.

Steve intends to conduct a one-way ANOVA ?-test at a significance level of ?=0.05 to test if the mean assessment test scores for the three training programs are all equal. The mean square between groups, MSG, is 176.1667 and the mean square within groups, also referred to as the mean square error, MSE, is 33.8444. Steve computes the ?-statistic, which is ?=5.2052.

Select the statement that accurately evaluates whether or not the requirements of a one-way ANOVA ?-test have been met in Steve's experiment. If the requirements have not been met, do not proceed to answer subsequent questions.

The requirements have been met because the sampling distributions are approximately normal and the dependent variable is categorical.

The requirements have not been met because the sample sizes are not properly selected and are not large enough.

The requirements have not been met because the population variances are unknown.

The requirements have been met because the samples are properly selected, are normally distributed, and of equal sizes.

The requirements have been met because the samples are properly selected and are approximately normally distributed with equal variances.

If the test requirements have been met, compute the degrees of freedom for the means square between groups, MSG, and the degress of freedom for the mean square error, MSE.

df1 =

df2 =

Determine the critical value of ? for Steve's hypothesis test at the significance level of ?=0.05 using software or an ?-distribution table. Give your answer to at least two decimal places.

?-critical value =

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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