(d) Compute a 95% confidence interval about the population mean difference Hd The lower bound is The upper bound is
(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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9286dec2-87de-41e0-b292-cb9e24765e4b%2F8c4cd155-f065-406e-9993-2c274bce3ecb%2Ftl06djj_processed.jpeg&w=3840&q=75)
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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