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 H₁ for the mean number of families with no children. At a=0.10, is there a difference between the means? Use the critical value method and tables. No children Children Send data to Excel X 847 10.6 6 2.6 2.9 n 32 32

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**Recreational Time Analysis**

A researcher is investigating whether there is a difference in the mean number of hours per week that a family with no children participates in recreational activities compared to a family with children. The researcher selected two random samples, and the data is as follows. Using a significance level of \(\alpha = 0.10\), the inquiry is to determine if there is a significant difference between the means using the critical value method.

**Data Summary:**

| Group        | Mean (\(\bar{X}\)) | Standard Deviation (\(\sigma\)) | Sample Size (\(n\)) |
|--------------|--------------------|---------------------------------|---------------------|
| No children  | 8.7                | 2.6                             | 32                  |
| Children     | 10.6               | 2.9                             | 32                  |

To conduct this analysis, compare the means of the two groups to see if the observed difference is statistically significant. This can be done using the critical value method and appropriate statistical tables.
Transcribed Image Text:**Recreational Time Analysis** A researcher is investigating whether there is a difference in the mean number of hours per week that a family with no children participates in recreational activities compared to a family with children. The researcher selected two random samples, and the data is as follows. Using a significance level of \(\alpha = 0.10\), the inquiry is to determine if there is a significant difference between the means using the critical value method. **Data Summary:** | Group | Mean (\(\bar{X}\)) | Standard Deviation (\(\sigma\)) | Sample Size (\(n\)) | |--------------|--------------------|---------------------------------|---------------------| | No children | 8.7 | 2.6 | 32 | | Children | 10.6 | 2.9 | 32 | To conduct this analysis, compare the means of the two groups to see if the observed difference is statistically significant. This can be done using the critical value method and appropriate statistical tables.
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