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What's test statistic and the p value?

What's test statistic and the p value?

MATLAB: An Introduction with Applications
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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What's test statistic and the p value?
### Statistical Hypothesis Testing and Confidence Interval Construction Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. #### Given Data: - **Population 1**: - \( n = 28 \) - \( \bar{x} = 45.7 \) - \( s = 5.4 \) - **Population 2**: - \( n = 21 \) - \( \bar{x} = 41.5 \) - \( s = 13.6 \) #### Tasks: (a) **Test whether \( \mu_1 > \mu_2 \) at the \( \alpha = 0.10 \) level of significance for the given sample data.** (b) **Construct a 90% confidence interval about \( \mu_1 - \mu_2 \).** --- #### (a) Identify the null and alternative hypotheses for this test. - Choose the correct statement: - A. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - B. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - C. \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - D. \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **E. \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 > \mu_2 \)** The correct choice is E, which implies testing if the mean of Population 1 is greater than the mean of Population 2. --- #### Find the test statistic for this hypothesis test. - **Round to two decimal places as needed.**
Transcribed Image Text:### Statistical Hypothesis Testing and Confidence Interval Construction Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. #### Given Data: - **Population 1**: - \( n = 28 \) - \( \bar{x} = 45.7 \) - \( s = 5.4 \) - **Population 2**: - \( n = 21 \) - \( \bar{x} = 41.5 \) - \( s = 13.6 \) #### Tasks: (a) **Test whether \( \mu_1 > \mu_2 \) at the \( \alpha = 0.10 \) level of significance for the given sample data.** (b) **Construct a 90% confidence interval about \( \mu_1 - \mu_2 \).** --- #### (a) Identify the null and alternative hypotheses for this test. - Choose the correct statement: - A. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - B. \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - C. \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - D. \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **E. \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 > \mu_2 \)** The correct choice is E, which implies testing if the mean of Population 1 is greater than the mean of Population 2. --- #### Find the test statistic for this hypothesis test. - **Round to two decimal places as needed.**
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