3. A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 14 female nurses reports the following data. Is there enough evidence to support the claim that male nurses earn more than female nurses? Use a = 0.05 and assume the population variances are equal. Please show all 4 steps of the classical approach clearly and interpret your conclusion. Male F₁ = $44.800 $1 = $300 71 = 16 Female 72 = $44.550 82 = $280 72₂ = 14
3. A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 14 female nurses reports the following data. Is there enough evidence to support the claim that male nurses earn more than female nurses? Use a = 0.05 and assume the population variances are equal. Please show all 4 steps of the classical approach clearly and interpret your conclusion. Male F₁ = $44.800 $1 = $300 71 = 16 Female 72 = $44.550 82 = $280 72₂ = 14
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Can someone please help me to solve the following question showing all work
![### Hypothesis Testing: Do Male Nurses Earn More Than Female Nurses?
A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 14 female nurses reports the following data. Is there enough evidence to support the claim that male nurses earn more than female nurses? Use \( \alpha = 0.05 \) and assume the population variances are equal. Please show all 4 steps of the **classical approach** clearly and interpret your conclusion.
#### Survey Data:
| | Male | Female |
|--------------------------|---------------------------------|---------------------------------|
| Sample Mean (\( \bar{x} \)) | $44,800 | $44,550 |
| Sample Standard Deviation (\( s \)) | $300 | $280 |
| Sample Size (\( n \)) | 16 | 14 |
### Steps for Hypothesis Testing
1. **State the Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( \mu_1 \leq \mu_2 \)
- (The mean salary of male nurses is less than or equal to the mean salary of female nurses.)
- Alternative Hypothesis (\( H_1 \)): \( \mu_1 > \mu_2 \)
- (The mean salary of male nurses is greater than the mean salary of female nurses.)
2. **Set the Significance Level (\( \alpha \)):**
- \( \alpha = 0.05 \)
3. **Compute the Test Statistic:**
Since we assume equal population variances, we will use the t-test for the comparison of two means:
\[
t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{s_p^2 \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}}
\]
Where the pooled sample variance \( s_p^2 \) is defined as:
\[
s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}
\]
Plugging in the given data:
\[
s_p^2 = \frac{(16-1)300^2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322ab9b5-8b73-42ca-a79a-5c7ee3611144%2F0b212456-5dae-4b27-91bf-87a771e09bba%2Fxnojjbr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Do Male Nurses Earn More Than Female Nurses?
A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 14 female nurses reports the following data. Is there enough evidence to support the claim that male nurses earn more than female nurses? Use \( \alpha = 0.05 \) and assume the population variances are equal. Please show all 4 steps of the **classical approach** clearly and interpret your conclusion.
#### Survey Data:
| | Male | Female |
|--------------------------|---------------------------------|---------------------------------|
| Sample Mean (\( \bar{x} \)) | $44,800 | $44,550 |
| Sample Standard Deviation (\( s \)) | $300 | $280 |
| Sample Size (\( n \)) | 16 | 14 |
### Steps for Hypothesis Testing
1. **State the Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( \mu_1 \leq \mu_2 \)
- (The mean salary of male nurses is less than or equal to the mean salary of female nurses.)
- Alternative Hypothesis (\( H_1 \)): \( \mu_1 > \mu_2 \)
- (The mean salary of male nurses is greater than the mean salary of female nurses.)
2. **Set the Significance Level (\( \alpha \)):**
- \( \alpha = 0.05 \)
3. **Compute the Test Statistic:**
Since we assume equal population variances, we will use the t-test for the comparison of two means:
\[
t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{s_p^2 \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}}
\]
Where the pooled sample variance \( s_p^2 \) is defined as:
\[
s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}
\]
Plugging in the given data:
\[
s_p^2 = \frac{(16-1)300^2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman