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 the0.05level 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 not92%. 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 not92%. 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 not92%. 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 not92%. **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.

Given data number of success , x= 189.0 sample size, n = 215 population proportion,p= 0.92 Significance level, α= 0.05Solution : a) Hypothesis test : The null and alternative hypothesis is Ho : p = 0.92 Ha : p ≠ 0.92b) np = 215 * 0.92 = 197.8 ≥ 10 n(1-p) = 215 * (1-0.92) = 17.2 ≥ 10 np ≥ 10 n(1-p) ≥ 10C) Test statistic : sample proportion p̂= x/n= 189.0 / 215 = 0.8791 Test statistic = 0.8791 - 0.92 /√( 0.92 (1- 0.92 )/ 215 = -2.211 The test statistic is -2.211 P-value : P-value =P(Z>|Zobs| = 2 x P(z < -2.211 )= 0.027 ---------- (from normal distribution z -table) ∴ P-value= 0.027 Excel output :D) 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%

Answered: This is part 'd' that isn't included in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

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