H 0 (b) For your hypothesis test, you will use a 2-test. Find the values of P and (1-p) to confirm that a Z-test can be used. (One standard is that p2 10 and 2 (1-p)210 under the assumption that the null hypothesis is true.) Here Iis the sample size and P is the population proportion you are testing. n (1-p) = 0 (C) Perform a Z-test. Here is some information to help you with your Z-test.
H 0 (b) For your hypothesis test, you will use a 2-test. Find the values of P and (1-p) to confirm that a Z-test can be used. (One standard is that p2 10 and 2 (1-p)210 under the assumption that the null hypothesis is true.) Here Iis the sample size and P is the population proportion you are testing. n (1-p) = 0 (C) Perform a Z-test. Here is some information to help you with your Z-test.
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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![The magazine Tech Worx reported that 93% 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 220 randomly chosen software engineers, 205 rated the company they work for as "a great place to work."
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support your claim that the proportion, \( p \), of all software engineers who rate the company they work for as "a great place to work" is not 93%.
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that you would use for the test.
- \( H_0: \)
- \( H_1: \)
(b) For your hypothesis test, you will use a Z-test. Find the values of \( np \) and \( n(1-p) \) to confirm that a Z-test can be used. (One standard is that \( np \ge 10 \) and \( n(1-p) \ge 10 \) under the assumption that the null hypothesis is true.) Here \( n \) is the sample size and \( p \) is the population proportion you are testing.
- \( np = \)
- \( n(1-p) = \)
(c) Perform a Z-test. Here is some information to help you with your Z-test.
- \( z_{0.025} \) is the value that cuts off an area of 0.025 in the right tail of the distribution.
- The value of the test statistic is given by \( z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}} \).
![Graph of Standard Normal Distribution] - This is a bell-shaped curve representing a standard normal distribution. The x-axis represents z-values, and the y-axis represents the probability density. There are marked areas under the curve to signify critical regions.
(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 value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the percentage of software engineers](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce1f951-db00-41fc-b226-5b8bf4ea58a6%2F82da10cb-aa4f-4958-b650-04a8fee2299d%2Frjvmck9_processed.png&w=3840&q=75)
Transcribed Image Text:The magazine Tech Worx reported that 93% 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 220 randomly chosen software engineers, 205 rated the company they work for as "a great place to work."
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support your claim that the proportion, \( p \), of all software engineers who rate the company they work for as "a great place to work" is not 93%.
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that you would use for the test.
- \( H_0: \)
- \( H_1: \)
(b) For your hypothesis test, you will use a Z-test. Find the values of \( np \) and \( n(1-p) \) to confirm that a Z-test can be used. (One standard is that \( np \ge 10 \) and \( n(1-p) \ge 10 \) under the assumption that the null hypothesis is true.) Here \( n \) is the sample size and \( p \) is the population proportion you are testing.
- \( np = \)
- \( n(1-p) = \)
(c) Perform a Z-test. Here is some information to help you with your Z-test.
- \( z_{0.025} \) is the value that cuts off an area of 0.025 in the right tail of the distribution.
- The value of the test statistic is given by \( z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}} \).
![Graph of Standard Normal Distribution] - This is a bell-shaped curve representing a standard normal distribution. The x-axis represents z-values, and the y-axis represents the probability density. There are marked areas under the curve to signify critical regions.
(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 value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the percentage of software engineers
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