(d) Compute a 95% confidence interval about the population mean difference Hd The lower bound is The upper bound is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 11MCQ
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complete part d

**Statistical Analysis of Normally Distributed Differences**

**Data Summary:**

- **Observations:**
  - **X\(_i\):** 53.4, 50.8, 50.7, 41.4, 51.4, 51.2, 45.2, 50.0
  - **Y\(_i\):** 54.7, 52.7, 54.5, 45.6, 51.8, 53.8, 45.8, 52.7

**Hypotheses:**

- **\(H_1: \mu_d > 0\)** (left-side)
- **\(H_1: \mu_d < 0\)** (right-side)

**Statistical Test:**

- **P-value:** 0.002 (rounded to three decimal places)

**Conclusion Options:**

- **A.** Reject the null hypothesis. There is insufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance.
- **B.** Do not reject the null hypothesis. There is insufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance.
- **C.** Reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance.
- **D.** Do not reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance.

**Correct Conclusion:**

- **C.** Reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance.

**Confidence Interval:**

- **(d)** Compute a 95% confidence interval for the population mean difference \(\mu_d\):
  - **Lower bound:** [ ] (to be rounded to two decimal places)
  - **Upper bound:** [ ] (to be rounded to two decimal places)
Transcribed Image Text:**Statistical Analysis of Normally Distributed Differences** **Data Summary:** - **Observations:** - **X\(_i\):** 53.4, 50.8, 50.7, 41.4, 51.4, 51.2, 45.2, 50.0 - **Y\(_i\):** 54.7, 52.7, 54.5, 45.6, 51.8, 53.8, 45.8, 52.7 **Hypotheses:** - **\(H_1: \mu_d > 0\)** (left-side) - **\(H_1: \mu_d < 0\)** (right-side) **Statistical Test:** - **P-value:** 0.002 (rounded to three decimal places) **Conclusion Options:** - **A.** Reject the null hypothesis. There is insufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance. - **B.** Do not reject the null hypothesis. There is insufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance. - **C.** Reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance. - **D.** Do not reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance. **Correct Conclusion:** - **C.** Reject the null hypothesis. There is sufficient evidence that \(\mu_d < 0\) at the \(\alpha = 0.05\) level of significance. **Confidence Interval:** - **(d)** Compute a 95% confidence interval for the population mean difference \(\mu_d\): - **Lower bound:** [ ] (to be rounded to two decimal places) - **Upper bound:** [ ] (to be rounded to two decimal places)
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