Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134508306

Author: Michael Sullivan III

Publisher: PEARSON

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Textbook Question

Chapter 11, Problem 4RE

In Problems 4 and 5, assume that the populations are normally distributed and that independent sampling occurred.

	Sample 1	Sample 2
n	13	8
x ¯	32.4	28.2
s	4.5	3.8

a. Test the hypothesis that μ₁ ≠ μ₂ at the α = 0.1 level of significance for the given sample data.
b. Construct a 90% confidence interval for μ₁ − μ₂.

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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Chapter 11, Problem 3RE

Chapter 11, Problem 5RE

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You wish to test the claim that the first population mean is greater than the second population mean at a significance level of α=0.05α=0.05. Ho:μ1=μ2 Ha:μ1>μ2 You obtain the following two samples of data. Sample #1 Sample #2 57.5 40.9 38.5 54.9 62.3 32.2 72.2 66.2 88.1 65.8 44.5 67.9 57.9 71.6 62.0 41.4 52.4 38.9 42.2 42.4 46.2 43.1 46.9 37.9 50.7 36.2 40.6 49.9 46.9 55.0 What is the test statistic for this sample?test statistic = Round to 3 decimal places. What is the p-value for this sample?p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.…

You wish to test the claim that the first population mean is less than the second population mean at a significance level of α=0.001. Ho:μ1=μ2 Ha:μ1<μ2 You obtain the following two samples of data. Sample #1 Sample #2 81.6 84.5 88.3 71.2 86.9 94.4 74.5 73.4 84.5 81.6 86.6 91.7 91.9 92.1 91.7 92.7 99.3 95.6 94.2 91.2 91.8 93.6 90.2 What is the test statistic for this sample?test statistic = Round to 3 decimal places. What is the p-value for this sample?p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. There is not sufficient evidence to warrant rejection of the…

You wish to test the claim that the first population mean is not equal to the second population mean at a significance level of α=0.02 . Ho:μ1=μ2 Ha:μ1≠μ2 You obtain the following two samples of data. Sample #1 Sample #2 67.1 64.2 32.7 49.0 63.8 54.8 63.5 54.1 65.6 54.8 40.5 58.7 39.4 43.1 72.5 73.1 70.2 71.2 68.1 73.1 79.7 67.3 66.5 61.7 62.9 76.5 What is the test statistic for this sample?test statistic = Round to 3 decimal places. What is the p-value for this sample?p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean. There is not sufficient…

Chapter 11 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - Prob. 8AYU Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...

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Solution Summary: The author concludes that there is sufficient evidence to support the claim that mu '_'1ne's_2 at the level of significance for the given sample data.

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