Answer:
To determine the rejection region for testing whether the mean in Statistics and Probability during the first quarter is greater than 39.5 with a 99% confidence level, you can use a one-sample t-test. The rejection region for a one-tailed hypothesis test will be in the upper tail of the t-distribution.
Here are the steps to find the rejection region:
1. Set up the hypotheses:
- Null Hypothesis (H0): μ ≤ 39.5 (claim that the mean is less than or equal to 39.5)
- Alternative Hypothesis (Ha): μ > 39.5 (claim that the mean is greater than 39.5)
2. Choose the significance level (alpha, α). In this case, it's 1 - Confidence Level, which is 0.01 (since the confidence level is 99%).
3. Find the critical value (t-critical) corresponding to α and degrees of freedom (df). The degrees of freedom depend on the sample size and are n - 1.
4. Calculate the test statistic (t-test) using the sample data.
5. Compare the test statistic to the critical value to decide whether to reject the null hypothesis.
To find the critical value, you can use a t-table or calculator. Since you want to find the critical value for a one-tailed test at a 99% confidence level and degrees of freedom (df) depend on your sample size, you'll need to know the sample size.
Assuming your sample size is n, the critical value (t-critical) for a one-tailed test at a 99% confidence level (α = 0.01) can be found using a t-table or calculator for df = n - 1 degrees of freedom.
Once you have the critical value, compare it to the calculated test statistic (t-test) from your sample data. If the test statistic is greater than the critical value, you'll reject the null hypothesis in favor of the alternative hypothesis. The rejection region is located in the right tail of the t-distribution.
Please provide the sample size (n) to proceed further and calculate the critical value and test statistic.
Explanation: