A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.58, s=0.59. Use a 0.05 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? O A. Ho: μ = 3.75 H₁:μ>3.75 O C. Ho: H=3.75 H₁: μ<3.75 Determine the test statistic. (Round to two decimal places as needed.) O B. Ho: μ#3.75 H₁: p=3.75 D. H₂:μ=3.75 H₁: μ#3.75

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A data set includes data from student evaluations of courses. The summary statistics are \( n = 89 \), \( \bar{x} = 3.58 \), \( s = 0.59 \). Use a 0.05 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.

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**What are the null and alternative hypotheses?**

- \( \text{A.} \quad H_0 : \mu = 3.75 \)
  \( \quad H_1 : \mu > 3.75 \)

- \( \text{B.} \quad H_0 : \mu \neq 3.75 \)
  \( \quad H_1 : \mu = 3.75 \)

- \( \text{C.} \quad H_0 : \mu = 3.75 \)
  \( \quad H_1 : \mu < 3.75 \)

- \( \text{D.} \quad H_0 : \mu = 3.75 \)
  \( \quad H_1 : \mu \neq 3.75 \)  ✅

**Determine the test statistic.**

- [ ] (Round to two decimal places as needed.)
Transcribed Image Text:A data set includes data from student evaluations of courses. The summary statistics are \( n = 89 \), \( \bar{x} = 3.58 \), \( s = 0.59 \). Use a 0.05 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?** - \( \text{A.} \quad H_0 : \mu = 3.75 \) \( \quad H_1 : \mu > 3.75 \) - \( \text{B.} \quad H_0 : \mu \neq 3.75 \) \( \quad H_1 : \mu = 3.75 \) - \( \text{C.} \quad H_0 : \mu = 3.75 \) \( \quad H_1 : \mu < 3.75 \) - \( \text{D.} \quad H_0 : \mu = 3.75 \) \( \quad H_1 : \mu \neq 3.75 \) ✅ **Determine the test statistic.** - [ ] (Round to two decimal places as needed.)
Expert Solution
Step 1: Given information

According to the given information, we have

Sample size, n =89Sample mean, x¯ = 3.58Sample standard deviation, s = 0.59Level of significance, α = 0.05

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