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Answer the following questions and give your answer to 3 decimal places accurately (ex. 1.999 or 1.000 or 1.850 etc) in the space below: (don't include any units and make use of a decimal point!) NB: Do not round intermediate calculations – only round at the end when you calculate the final answer! Make use of the t-Tables & Standard Normal Tables provided on clickUP.

Calculate the p-value for this test: Blank 1 < p-value < Blank 2

To calculate the p-value for this test, let's go through the given information:

- **Sample size (n)** = 57
- **Sample mean (\(\bar{x}\))** = 16.42
- **Standard deviation (s)** = 6.55
- **Test statistic (t)** = 1.637 (rounded from 1.6368)
- **Significance level (\(\alpha\))** = 0.05

The test is for whether the mean hours of outdoor activities is **greater than 15**. Since this is a one-tailed test, we need to determine the p-value for the given test statistic (1.637) under a t-distribution with **degrees of freedom (df) = n - 1 = 57 - 1 = 56**.

### Step 1: Look up the t-distribution table
Using the t-distribution table for \(df = 56\), we need to find the range of p-values for \(t = 1.637\).

Since we may not have direct access to 56 degrees of freedom on most standard tables, you can often use 55 or 60 for approximation:

- For **t = 1.637** with **df = 56**, the p-value lies between 0.05 and 0.10 in a one-tailed test, based on the closest values in a typical t-table.

### Conclusion
So, we can conclude the following:

- **Blank 1 (lower bound)** = 0.05
- **Blank 2 (upper bound)** = 0.10

The p-value lies between 0.05 and 0.10.

Let me know if you have more questions or would like further explanation on any part of this!

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**Additional Related Questions:**

1. How would the p-value change if we were conducting a two-tailed test instead?
2. What is the critical t-value for a one-tailed test with \(\alpha = 0.05\) and 56 degrees of freedom?
3. How does the sample size affect the width of the confidence interval in a t-test?
4. Why is it important not to round intermediate calculations until the final step?
5. What assumptions are made in a t-test for a sample mean?

**Tip:** For higher accuracy, always refer to a detailed t-table or statistical software, especially when degrees of freedom don't match exactly with standard tables.

Learn how to calculate the p-value for a one-tailed hypothesis test using a t-distribution with a sample size of 57, mean of 16.42, standard deviation of 6.55, and a test statistic of 1.6368. Determine if the average hours students spend on outdoor activities per month exceed 15 hours.

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