8. The average amount of time boys and girls ages 7 through 11 spend playing sports each day is believed to be the same. An experiment is done, data is collected, resulting in the data below: Sample Size Average Number of Hours Playing Sports Per Day Of 32 girls, the average number hours playing sports is 2 with a standard deviation of 0.75. Of 35 boys, the average number hours playing sports is 3.2 with a standard deviation of 1. there a difference in the average amount of time boys and girls ages 7 through 11 play sports ach day? Test at the 5% level of significance. (You DO NOT need to show all steps- just state est statistic, p-value versus alpha, formal conclusion and practical conclusion in a complete entence)
8. The average amount of time boys and girls ages 7 through 11 spend playing sports each day is believed to be the same. An experiment is done, data is collected, resulting in the data below: Sample Size Average Number of Hours Playing Sports Per Day Of 32 girls, the average number hours playing sports is 2 with a standard deviation of 0.75. Of 35 boys, the average number hours playing sports is 3.2 with a standard deviation of 1. there a difference in the average amount of time boys and girls ages 7 through 11 play sports ach day? Test at the 5% level of significance. (You DO NOT need to show all steps- just state est statistic, p-value versus alpha, formal conclusion and practical conclusion in a complete entence)
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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Need help with number 8 and 9 I don’t quite understand the question.
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### Transcription and Analysis of Hypothesis Testing Scenarios
**Problem 8: Comparing Sports Activity Between Boys and Girls**
The aim is to determine if there is a difference in the average amount of time boys and girls aged 7 through 11 spend playing sports each day. An experiment is conducted and data is collected as follows:
- **Sample Size and Average Number of Hours Playing Sports Per Day:**
- **Girls:** 32 students, with an average of 2 hours per day (standard deviation of 0.75).
- **Boys:** 35 students, with an average of 3.2 hours per day (standard deviation of 1).
To test the hypothesis at the 5% level of significance, one would:
- Compare the means of the two groups.
- Decide on the null hypothesis (\(H_0\))—no difference in average times—and the alternative hypothesis (\(H_a\))—there is a difference.
- Without showing all calculations, one would calculate the test statistic and p-value.
- Compare the p-value to the significance level (\( \alpha = 0.05\)).
- Draw conclusions based on whether the null hypothesis is rejected or not.
**Problem 9: Impact of Calcium Supplements on Blood Pressure**
A medical researcher investigates the effects of calcium supplements on men's diastolic blood pressure. The study involves 10 men with measurements taken before and after a 12-week supplement regimen. The diastolic blood pressures recorded are as follows:
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---------|----|----|----|----|----|----|----|----|----|----|
| Before | 107| 110| 123| 129| 112| 111| 107| 112| 136| 102 |
| After | 100| 114| 105| 112| 115| 116| 107| 112| 135| 100 |
To test the hypothesis at \(\alpha = 0.10\), the following steps are suggested:
- Set up hypotheses: The null hypothesis (\(H_0\)) states that there is no difference in blood
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