Recreational Time A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ₁ for the mean number of families with no children. At a=0.01, is there a difference between the means? Use the critical value method and tables. X O n No children 8.8 2.4 34 Children 10.4 2.9 34 Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho: (Choose one) ▼ H₁: (Choose one) This hypothesis test is a (Choose one) ▼ test. Send data to Excel
Recreational Time A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ₁ for the mean number of families with no children. At a=0.01, is there a difference between the means? Use the critical value method and tables. X O n No children 8.8 2.4 34 Children 10.4 2.9 34 Part: 0/5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho: (Choose one) ▼ H₁: (Choose one) This hypothesis test is a (Choose one) ▼ test. Send data to Excel
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
State the hypothesis and identify the claim. Find the critical and z-values.
![### Recreational Time Study
A researcher wishes to determine if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. The researcher selects two random samples and the data are shown below. Use \(\mu_1\) for the mean number of hours for families with no children. At \(\alpha = 0.01\), is there a difference between the means? Use the critical value method and tables.
#### Data Summary:
| Group | \(\bar{X}\) (Mean) | \(\sigma\) (Standard Deviation) | \(n\) (Sample Size) |
|---------------|-------------------|------------------------------|---------------------|
| No children | 8.8 | 2.4 | 34 |
| Children | 10.4 | 2.9 | 34 |
#### Task (Part 1 of 5):
(a) State the hypotheses and identify the claim.
- Null Hypothesis (\(H_0\)): [Choose one]
- Alternative Hypothesis (\(H_1\)): [Choose one]
This hypothesis test is a [Choose one] test.
#### Explanation of the Table:
The table presents the data comparison between the families with no children and families with children in terms of:
- Mean hours per week spent on recreational activities (\(\bar{X}\)).
- Standard deviation (\(\sigma\)) of hours spent on recreational activities.
- Number of families sampled (n).
The objective is to test if the mean hours differ significantly between the two groups at a 0.01 significance level using the critical value method to determine if there is a statistically significant difference between the two means.
#### Steps Overview for Hypothesis Testing:
1. State the Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
2. State the Alternative Hypothesis (\(H_1\)): \( \mu_1 \neq \mu_2 \)
3. Determine the significance level (\(\alpha = 0.01\)).
4. Calculate the test statistic.
5. Compare the test statistic to the critical value.
6. Draw a conclusion about the hypotheses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08ad6c20-d691-4a3f-8949-0fe4518b5718%2Fcc3b0676-75f7-4460-8cbd-9dcbd53ed6ea%2F1vk16j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Recreational Time Study
A researcher wishes to determine if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. The researcher selects two random samples and the data are shown below. Use \(\mu_1\) for the mean number of hours for families with no children. At \(\alpha = 0.01\), is there a difference between the means? Use the critical value method and tables.
#### Data Summary:
| Group | \(\bar{X}\) (Mean) | \(\sigma\) (Standard Deviation) | \(n\) (Sample Size) |
|---------------|-------------------|------------------------------|---------------------|
| No children | 8.8 | 2.4 | 34 |
| Children | 10.4 | 2.9 | 34 |
#### Task (Part 1 of 5):
(a) State the hypotheses and identify the claim.
- Null Hypothesis (\(H_0\)): [Choose one]
- Alternative Hypothesis (\(H_1\)): [Choose one]
This hypothesis test is a [Choose one] test.
#### Explanation of the Table:
The table presents the data comparison between the families with no children and families with children in terms of:
- Mean hours per week spent on recreational activities (\(\bar{X}\)).
- Standard deviation (\(\sigma\)) of hours spent on recreational activities.
- Number of families sampled (n).
The objective is to test if the mean hours differ significantly between the two groups at a 0.01 significance level using the critical value method to determine if there is a statistically significant difference between the two means.
#### Steps Overview for Hypothesis Testing:
1. State the Null Hypothesis (\(H_0\)): \( \mu_1 = \mu_2 \)
2. State the Alternative Hypothesis (\(H_1\)): \( \mu_1 \neq \mu_2 \)
3. Determine the significance level (\(\alpha = 0.01\)).
4. Calculate the test statistic.
5. Compare the test statistic to the critical value.
6. Draw a conclusion about the hypotheses.
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