ProctoredNonproctored study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not ssume that the population standard deviations are equal. Complete parts (a) and (b) below. P2 n x 76.73 s 10.36 31 30 86.11 19.04 Use a 0.05 significance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. hat are the null and alternative hypotheses? OA. Ho H2 O B. Ho P =P2 H P

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Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.__<μ1−μ2<__​(Round to three decimal places as​ needed.)

Title: Hypothesis Testing for Proctored vs Nonproctored Tests

A study was conducted on proctored and nonproctored tests. The results are displayed in the table, assuming the samples are independent simple random samples from normally distributed populations, without assuming equal population standard deviations. Complete parts (a) and (b) based on the information.

---

**a. Use a 0.05 significance level to test the claim that students taking nonproctored tests achieve a higher mean score than those taking proctored tests.**

**Hypotheses:**

What are the null and alternative hypotheses?

- **A.**  
  \( H_0: \mu_1 \neq \mu_2 \)  
  \( H_1: \mu_1 < \mu_2 \)

- **B.**  
  \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 \neq \mu_2 \)

- **C.**  
  \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 < \mu_2 \)  
  *(Correct Choice)*

- **D.**  
  \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 > \mu_2 \)

**The test statistic, \( t \), is** \( \square \). (Round to two decimal places as needed.)

---

**Table Explanation:**

|            | Proctored (\( \mu_1 \)) | Nonproctored (\( \mu_2 \)) |
|------------|-------------------------|----------------------------|
| \( n \)    | 31                      | 30                         |
| \( \bar{x} \)  | 76.73                   | 86.11                      |
| \( s \)    | 10.36                   | 19.04                      |

- \( n \) is the sample size.
- \( \bar{x} \) is the mean score.
- \( s \) is the standard deviation of the scores.

This setup will guide you through testing the hypothesis that nonproctored tests lead to higher scores, using the provided statistical data.
Transcribed Image Text:Title: Hypothesis Testing for Proctored vs Nonproctored Tests A study was conducted on proctored and nonproctored tests. The results are displayed in the table, assuming the samples are independent simple random samples from normally distributed populations, without assuming equal population standard deviations. Complete parts (a) and (b) based on the information. --- **a. Use a 0.05 significance level to test the claim that students taking nonproctored tests achieve a higher mean score than those taking proctored tests.** **Hypotheses:** What are the null and alternative hypotheses? - **A.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 < \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - **C.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \) *(Correct Choice)* - **D.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) **The test statistic, \( t \), is** \( \square \). (Round to two decimal places as needed.) --- **Table Explanation:** | | Proctored (\( \mu_1 \)) | Nonproctored (\( \mu_2 \)) | |------------|-------------------------|----------------------------| | \( n \) | 31 | 30 | | \( \bar{x} \) | 76.73 | 86.11 | | \( s \) | 10.36 | 19.04 | - \( n \) is the sample size. - \( \bar{x} \) is the mean score. - \( s \) is the standard deviation of the scores. This setup will guide you through testing the hypothesis that nonproctored tests lead to higher scores, using the provided statistical data.
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