b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women. (Round to three decimal places as needed.) Does the confidence interval support the conclusion found with the hypothesis test? because the confidence interval contains

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Q2B

Hi wonderful Bartleby team, I need help with this two final parts of the exercise of completing the sentence and the last part of it as well (both marked in red)

Sentense says:

( Yes, No )because the confidence interval contains(Only positives / Only Negatives / Zero )

A study was conducted on the body temperatures of men and women. The table below displays the results. The two samples are independent simple random samples from normally distributed populations, and the population standard deviations are equal.

|        | Men (μ₁)  | Women (μ₂) |
|--------|-----------|------------|
| n      | 11        | 59         |
| x̄     | 97.68°F   | 97.35°F    |
| s      | 0.97°F    | 0.71°F     |

### Task a: Hypothesis Testing

Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women.

**Null and Alternative Hypotheses:**

- A: \( H_0: \mu_1 \geq \mu_2 \), \( H_1: \mu_1 < \mu_2 \)
- B: \( H_0: \mu_1 \neq \mu_2 \), \( H_1: \mu_1 < \mu_2 \)
- C: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \)
- D: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \)

**Chosen Hypotheses:**

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

**Test Statistic:**

- \( t \) = 1.33 (rounded to two decimal places)

**P-value:**

- 0.094 (rounded to three decimal places)

**Conclusion:**

- Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

### Task b: Confidence Interval

Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

- \( < \mu_1 - \mu_2 < \) (round to three decimal places)

**Does the confidence interval support the conclusion from the hypothesis test?**

- Choose the correct option: [Drop-down box]

(Note: The exact values for the confidence interval and the final decision on
Transcribed Image Text:A study was conducted on the body temperatures of men and women. The table below displays the results. The two samples are independent simple random samples from normally distributed populations, and the population standard deviations are equal. | | Men (μ₁) | Women (μ₂) | |--------|-----------|------------| | n | 11 | 59 | | x̄ | 97.68°F | 97.35°F | | s | 0.97°F | 0.71°F | ### Task a: Hypothesis Testing Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. **Null and Alternative Hypotheses:** - A: \( H_0: \mu_1 \geq \mu_2 \), \( H_1: \mu_1 < \mu_2 \) - B: \( H_0: \mu_1 \neq \mu_2 \), \( H_1: \mu_1 < \mu_2 \) - C: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 \neq \mu_2 \) - D: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \) **Chosen Hypotheses:** - D: \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \) **Test Statistic:** - \( t \) = 1.33 (rounded to two decimal places) **P-value:** - 0.094 (rounded to three decimal places) **Conclusion:** - Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. ### Task b: Confidence Interval Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women. - \( < \mu_1 - \mu_2 < \) (round to three decimal places) **Does the confidence interval support the conclusion from the hypothesis test?** - Choose the correct option: [Drop-down box] (Note: The exact values for the confidence interval and the final decision on
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman