A data set includes data from student evaluations of courses. The summary statistics are n=83, x= 3.65, s=0.51. Use a 0.10 significance level to test the Claim that the population of student course evaluations has a mean equal to 3.75. 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? OA. Ho: H=3.75 ( H₁>3.75 OC. Ho: 3.75 H₁: = 3.75 Determine the test statistic. (Round to two decimal places as needed.) OB. Ho: H=3.75 H, μ<3.75 D. Ho: H=3.75 H₁: μ#3.75

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### Hypothesis Testing on Student Course Evaluations

A data set includes data from student evaluations of courses. The summary statistics are as follows:

- Sample size (\(n\)) = 83
- Sample mean (\(\bar{x}\)) = 3.65
- Sample standard deviation (\(s\)) = 0.51

Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. 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?

- **Option A**
  - \(H_0\): \(\mu = 3.75\)
  - \(H_1\): \(\mu > 3.75\)

- **Option B**
  - \(H_0\): \(\mu = 3.75\)
  - \(H_1\): \(\mu < 3.75\)

- **Option C**
  - \(H_0\): \(\mu \neq 3.75\)
  - \(H_1\): \(\mu = 3.75\)

- **Option D (Selected)**
  - \(H_0\): \(\mu = 3.75\)
  - \(H_1\): \(\mu \neq 3.75\)

#### Determine the test statistic.

- Round to two decimal places as needed.
Transcribed Image Text:### Hypothesis Testing on Student Course Evaluations A data set includes data from student evaluations of courses. The summary statistics are as follows: - Sample size (\(n\)) = 83 - Sample mean (\(\bar{x}\)) = 3.65 - Sample standard deviation (\(s\)) = 0.51 Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. 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? - **Option A** - \(H_0\): \(\mu = 3.75\) - \(H_1\): \(\mu > 3.75\) - **Option B** - \(H_0\): \(\mu = 3.75\) - \(H_1\): \(\mu < 3.75\) - **Option C** - \(H_0\): \(\mu \neq 3.75\) - \(H_1\): \(\mu = 3.75\) - **Option D (Selected)** - \(H_0\): \(\mu = 3.75\) - \(H_1\): \(\mu \neq 3.75\) #### Determine the test statistic. - Round to two decimal places as needed.
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