Student	Movies	Sports	Parties
1	8	4	26
2	7	3	10
3	10	23	10
4	2	10	55
5	13	3	12
6	6	9	33
7	43	12	51
8	0	26	6
9	22	4	26
10	10	12	0
The 95​% confidence interval is
The test statistic is tequals
The​ P-value is

To analyze this data and calculate the 95% confidence interval, test statistic, and P-value, we'll follow these steps:

1. **Determine the Sample Mean (\(\bar{x}\)) and Standard Deviation (\(s\)):**
   - First, calculate the means and standard deviations for each column (Movies, Sports, Parties).

2. **Formulate the Hypothesis:**
   - Null Hypothesis (\(H_0\)): There is no significant difference in the means of the different activities (Movies, Sports, Parties).
   - Alternative Hypothesis (\(H_a\)): There is a significant difference in the means of the different activities.

3. **Calculate the Test Statistic:**
   - If the data follows a normal distribution, use a t-test for comparing means. The test statistic can be calculated using:
     \[
     t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
     \]
   - Where \(\bar{x}_1\) and \(\bar{x}_2\) are the sample means of the two groups, \(s_1\) and \(s_2\) are their standard deviations, and \(n_1\) and \(n_2\) are the sample sizes.

4. **Calculate the 95% Confidence Interval:**
   - The confidence interval for the difference between two means can be calculated using:
     \[
     (\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2, \, df} \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
     \]

5. **Find the P-Value:**
   - The P-value is determined based on the test statistic and the degrees of freedom (df), using a t-distribution table or software.

Let's calculate these values. Do you have a specific comparison or pair of activities you'd like to compare, or should I select a common pair like "Movies vs. Sports"?

Would you like to proceed with the calculations or need further details on these steps?

Learn how to analyze data on student activities including movies, sports, and parties. Calculate the 95% confidence interval, test statistic, and P-value for comparing means using statistical methods. Suitable for advanced high school or college students.

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