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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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### Do the Poor Spend the Same Amount of Time in the Shower as the Rich? A survey was conducted to determine if there is a difference in the amount of time that poor and rich people spend in the shower. The results are as follows: #### Poor (minutes spent in the shower): 9, 37, 37, 26, 30, 17, 21, 13, 26, 33, 30 #### Rich (minutes spent in the shower): 42, 23, 19, 55, 24, 18, 38, 47, 27, 48, 19, 49 ### Statistical Analysis Assume both sets of data follow a normal distribution. We will use a two-sample t-test to determine if there is a significant difference in the mean shower time between the two groups at the α = 0.01 level of significance. For this study, we should use a **t-test for the difference between two independent population means**. #### Hypotheses 1. **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \) (The mean shower time for poor people is equal to the mean shower time for rich people.) 2. **Alternative Hypothesis (H₁):** \( \mu_1 \neq \mu_2 \) (The mean shower time for poor people is not equal to the mean shower time for rich people.) #### Test Statistic \( t = \) (Please show your answer to 3 decimal places.) #### P-value The p-value is used to determine the significance of the results. \( p \text{ value} = \) (Please show your answer to 3 decimal places.)
Transcribed Image Text:### Do the Poor Spend the Same Amount of Time in the Shower as the Rich? A survey was conducted to determine if there is a difference in the amount of time that poor and rich people spend in the shower. The results are as follows: #### Poor (minutes spent in the shower): 9, 37, 37, 26, 30, 17, 21, 13, 26, 33, 30 #### Rich (minutes spent in the shower): 42, 23, 19, 55, 24, 18, 38, 47, 27, 48, 19, 49 ### Statistical Analysis Assume both sets of data follow a normal distribution. We will use a two-sample t-test to determine if there is a significant difference in the mean shower time between the two groups at the α = 0.01 level of significance. For this study, we should use a **t-test for the difference between two independent population means**. #### Hypotheses 1. **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \) (The mean shower time for poor people is equal to the mean shower time for rich people.) 2. **Alternative Hypothesis (H₁):** \( \mu_1 \neq \mu_2 \) (The mean shower time for poor people is not equal to the mean shower time for rich people.) #### Test Statistic \( t = \) (Please show your answer to 3 decimal places.) #### P-value The p-value is used to determine the significance of the results. \( p \text{ value} = \) (Please show your answer to 3 decimal places.)
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