A data set includes data from student evaluations of courses. The summary statistics are n=85, x=4.07, s = 0.68. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. 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? O A. Ho: H=425 O B. Ho u=4.25 H, µ> 4.25 D. Ho: u=4.25 H: µ<4.25 OC. Ho: H#4.25 H:p=4.25 H, u+4 25 Determine the test statistic. O(Round to two decimal places as needed.)

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Can you help me find the test statistics and p-value
**Hypothesis Testing Example**

A dataset includes data from student evaluations of courses. The summary statistics are:
- Sample size (\( n \)): 85
- Sample mean (\( \bar{x} \)): 4.07
- Standard deviation (\( s \)): 0.68

We use a significance level of 0.05 to test the claim that the population of student course evaluations has a mean equal to 4.25. Assume that a simple random sample has been selected. 

Identify the null and alternative hypotheses, calculate the test statistic, find the P-value, and state the final conclusion that addresses the original claim.

### What are the null and alternative hypotheses?

#### Options:
- **A.** 
  - \( H_0: \mu = 4.25 \) 
  - \( H_1: \mu < 4.25 \)

- **B.** 
  - \( H_0: \mu = 4.25 \) 
  - \( H_1: \mu > 4.25 \)

- **C.** 
  - \( H_0: \mu \neq 4.25 \) 
  - \( H_1: \mu = 4.25 \)

- **D.** 
  - \( H_0: \mu = 4.25 \) 
  - \( H_1: \mu \neq 4.25 \)

The correct choice is **D**, where the null hypothesis \( H_0 \) claims that the mean is 4.25, and the alternative hypothesis \( H_1 \) claims that the mean is not equal to 4.25.

### Determine the test statistic.

(Instructions on rounding: Round to two decimal places as needed.)

There is a checkbox to enter your answer and then click "Check Answer."

**Progress Status:** 2 parts remaining

Use this information to evaluate the claim about the population mean and draw the appropriate conclusion.
Transcribed Image Text:**Hypothesis Testing Example** A dataset includes data from student evaluations of courses. The summary statistics are: - Sample size (\( n \)): 85 - Sample mean (\( \bar{x} \)): 4.07 - Standard deviation (\( s \)): 0.68 We use a significance level of 0.05 to test the claim that the population of student course evaluations has a mean equal to 4.25. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, calculate the test statistic, find the P-value, and state the final conclusion that addresses the original claim. ### What are the null and alternative hypotheses? #### Options: - **A.** - \( H_0: \mu = 4.25 \) - \( H_1: \mu < 4.25 \) - **B.** - \( H_0: \mu = 4.25 \) - \( H_1: \mu > 4.25 \) - **C.** - \( H_0: \mu \neq 4.25 \) - \( H_1: \mu = 4.25 \) - **D.** - \( H_0: \mu = 4.25 \) - \( H_1: \mu \neq 4.25 \) The correct choice is **D**, where the null hypothesis \( H_0 \) claims that the mean is 4.25, and the alternative hypothesis \( H_1 \) claims that the mean is not equal to 4.25. ### Determine the test statistic. (Instructions on rounding: Round to two decimal places as needed.) There is a checkbox to enter your answer and then click "Check Answer." **Progress Status:** 2 parts remaining Use this information to evaluate the claim about the population mean and draw the appropriate conclusion.
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