A data set includes data from student evaluations of courses. The summary statistics are n= 94, x= 3.41, s=0.64. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? Ο Α. H μ= 3.50 O B. Ho: H= 3.50 H,:p> 3.50 H: u#3.50 O C. Ho: H#3.50 O D. Ho: H=3.50 H: u= 3.50 H,:p<3.50 Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) <> State the final conclusion that addresses the original claim. Ho. There evidence to conclude that the original claim that the mean of the population of student course evaluations is equal to 3.50 correct.

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The dataset includes data from student evaluations of courses. The summary statistics are as follows: sample size \( n = 94 \), sample mean \( \bar{x} = 3.41 \), and sample standard deviation \( s = 0.64 \). A significance level of 0.05 is used to test the claim that the population of student course evaluations has a mean equal to 3.50. It is assumed that a simple random sample has been selected. The task is to identify the null and alternative hypotheses, calculate the test statistic, determine the P-value, and state the final conclusion addressing the original claim.

**Null and Alternative Hypotheses Options:**

- **A.**
  - \( H_0: \mu = 3.50 \)
  - \( H_1: \mu \neq 3.50 \)

- **B.**
  - \( H_0: \mu = 3.50 \)
  - \( H_1: \mu > 3.50 \)

- **C.**
  - \( H_0: \mu \neq 3.50 \)
  - \( H_1: \mu = 3.50 \)

- **D.**
  - \( H_0: \mu = 3.50 \)
  - \( H_1: \mu < 3.50 \)

**Steps to Follow:**

1. **Determine the Test Statistic:**
   - The test statistic should be rounded to two decimal places as needed.

2. **Determine the P-value:**
   - The P-value should be rounded to three decimal places as needed.

3. **State the Final Conclusion:**
   - A statement should be made regarding the evidence to conclude whether the original claim that the mean of the population of student course evaluations is equal to 3.50 is correct or not.

**Note:** The outlined process involves selecting the appropriate hypotheses, performing calculations as per statistical methods, and interpreting results to reach a conclusion based on the significance level.
Transcribed Image Text:The dataset includes data from student evaluations of courses. The summary statistics are as follows: sample size \( n = 94 \), sample mean \( \bar{x} = 3.41 \), and sample standard deviation \( s = 0.64 \). A significance level of 0.05 is used to test the claim that the population of student course evaluations has a mean equal to 3.50. It is assumed that a simple random sample has been selected. The task is to identify the null and alternative hypotheses, calculate the test statistic, determine the P-value, and state the final conclusion addressing the original claim. **Null and Alternative Hypotheses Options:** - **A.** - \( H_0: \mu = 3.50 \) - \( H_1: \mu \neq 3.50 \) - **B.** - \( H_0: \mu = 3.50 \) - \( H_1: \mu > 3.50 \) - **C.** - \( H_0: \mu \neq 3.50 \) - \( H_1: \mu = 3.50 \) - **D.** - \( H_0: \mu = 3.50 \) - \( H_1: \mu < 3.50 \) **Steps to Follow:** 1. **Determine the Test Statistic:** - The test statistic should be rounded to two decimal places as needed. 2. **Determine the P-value:** - The P-value should be rounded to three decimal places as needed. 3. **State the Final Conclusion:** - A statement should be made regarding the evidence to conclude whether the original claim that the mean of the population of student course evaluations is equal to 3.50 is correct or not. **Note:** The outlined process involves selecting the appropriate hypotheses, performing calculations as per statistical methods, and interpreting results to reach a conclusion based on the significance level.
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