This is part 'd' that isn't included in the picture. (d)Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about your claim.     Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the percentage of software engineers who rate the company they work for as "a great place to work" is not 92% .

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

This is part 'd' that isn't included in the picture.

(d)Based on your answer to part (c), choose what can be concluded, at the
0.05
level of significance, about your claim.
 
 
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the percentage of software engineers who rate the company they work for as "a great place to work" is not
92%
.
 
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the percentage of software engineers who rate the company they work for as "a great place to work" is not
92%
.
 
Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the percentage of software engineers who rate the company they work for as "a great place to work" is not
92%
.
 
Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the percentage of software engineers who rate the company they work for as "a great place to work" is not
92%
.
**Educational Website: Hypothesis Testing Example**

**Background:**
The magazine Tech Worx reported that 92% of software engineers rate the company they work for as "a great place to work." As a veteran headhunter, you claim the percentage given in the report is not correct. In a survey of 215 randomly chosen software engineers, 189 rated the company they work for as "a great place to work."

**Objective:**
To test if the proportion, \( p \), of all software engineers who rate the company they work for as "a great place to work" is not 92%.

---

**Steps for Hypothesis Testing:**

**(a) Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p = 0.92 \)
- Alternative Hypothesis (\( H_1 \)): \( p \neq 0.92 \)

**(b) Z-Test Requirements:**
Perform a Z-test by confirming \( np \) and \( n(1-p) \): 

**Parameters:**
- \( n = 215 \) (sample size)
- \( p = 0.92 \) (population proportion under null hypothesis)

Ensure both \( np \) and \( n(1-p) \) are greater than 10.

**(c) Z-Test Calculation:**

- **Formula for Test Statistic:**
  \[
  Z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}
  \]

- Calculate the test statistic and find the corresponding p-value.

**Graph Description:**
A standard normal distribution curve is depicted, where areas under the curve correspond to p-values.

**Steps:**
1. Enter the test statistic (round to 3 decimal places).
2. Shade the area represented by the p-value.
3. Enter the p-value (round to 3 decimal places).

**(d) Conclusion:**
Based on the p-value obtained from part (c), determine if the null hypothesis can be rejected at the 0.05 level of significance. Depending on the result, conclude if there is enough evidence to suggest the proportion is not 92%.

This method helps in assessing the validity of statistical claims within a specified confidence level.
Transcribed Image Text:**Educational Website: Hypothesis Testing Example** **Background:** The magazine Tech Worx reported that 92% of software engineers rate the company they work for as "a great place to work." As a veteran headhunter, you claim the percentage given in the report is not correct. In a survey of 215 randomly chosen software engineers, 189 rated the company they work for as "a great place to work." **Objective:** To test if the proportion, \( p \), of all software engineers who rate the company they work for as "a great place to work" is not 92%. --- **Steps for Hypothesis Testing:** **(a) Hypotheses:** - Null Hypothesis (\( H_0 \)): \( p = 0.92 \) - Alternative Hypothesis (\( H_1 \)): \( p \neq 0.92 \) **(b) Z-Test Requirements:** Perform a Z-test by confirming \( np \) and \( n(1-p) \): **Parameters:** - \( n = 215 \) (sample size) - \( p = 0.92 \) (population proportion under null hypothesis) Ensure both \( np \) and \( n(1-p) \) are greater than 10. **(c) Z-Test Calculation:** - **Formula for Test Statistic:** \[ Z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}} \] - Calculate the test statistic and find the corresponding p-value. **Graph Description:** A standard normal distribution curve is depicted, where areas under the curve correspond to p-values. **Steps:** 1. Enter the test statistic (round to 3 decimal places). 2. Shade the area represented by the p-value. 3. Enter the p-value (round to 3 decimal places). **(d) Conclusion:** Based on the p-value obtained from part (c), determine if the null hypothesis can be rejected at the 0.05 level of significance. Depending on the result, conclude if there is enough evidence to suggest the proportion is not 92%. This method helps in assessing the validity of statistical claims within a specified confidence level.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE 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