Find the standard score (round to two decimal places as needed) z= Find the P-value (round to four decimal places as needed) P-value= Make an conclusion
Find the standard score (round to two decimal places as needed) z= Find the P-value (round to four decimal places as needed) P-value= Make an conclusion
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
Please don't forget to read this! There are 3 more parts to the question.
Find the standard score (round to two decimal places as needed)
z=
Find the P-value (round to four decimal places as needed)
P-value=
Make an conclusion
![### Hypothesis Testing for Compulsive Buyers Questionnaire Scores
#### Problem Statement
A random sample of 36 subjects who identified themselves as compulsive buyers was obtained and given a questionnaire. They had a mean questionnaire score of 0.59 with a standard deviation of 0.18. Test the claim that the population of self-identified compulsive buyers has a mean greater than the mean of 0.51 for the general population. Use a 0.05 significance level.
---
#### Step 1: State the Null and Alternative Hypotheses
Select the correct null and alternative hypotheses for the test:
**A.** \( H_0: \mu = 0.51 \)
\[ H_a: \mu < 0.51 \]
**B.** (Correct)
\[ H_0: \mu = 0.51 \]
\[ H_a: \mu > 0.51 \]
**C.**
\[ H_0: \mu \neq 0.51 \]
\[ H_a: \mu = 0.51 \]
**D.**
\[ H_0: \mu = 0.51 \]
\[ H_a: \mu \neq 0.51 \]
---
#### Step 2: Calculate the Z-Score
Using the provided data:
- Sample Mean (\( \bar{x} \)) = 0.59
- Population Mean (\( \mu \)) = 0.51
- Standard Deviation (\( \sigma \)) = 0.18
- Sample Size (\( n \)) = 36
First, find the Standard Error (SE):
\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.18}{\sqrt{36}} = \frac{0.18}{6} = 0.03 \]
Then, calculate the Z-score:
\[ Z = \frac{\bar{x} - \mu}{SE} = \frac{0.59 - 0.51}{0.03} = \frac{0.08}{0.03} = 2.67 \]
So, the Z-score is:
\[ Z = \boxed{2.67} \]
*(Round to two decimal places as needed.)*
---
This Z-score can be used in further steps to determine the corresponding p-value, and to conclude whether there is sufficient evidence to reject the null hypothesis in favor of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a448b68-b882-4133-a49b-44585a3f695e%2Fd8cc71ba-ad58-4295-af1c-e6ca8d98b6ba%2Fjbwq2i_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Compulsive Buyers Questionnaire Scores
#### Problem Statement
A random sample of 36 subjects who identified themselves as compulsive buyers was obtained and given a questionnaire. They had a mean questionnaire score of 0.59 with a standard deviation of 0.18. Test the claim that the population of self-identified compulsive buyers has a mean greater than the mean of 0.51 for the general population. Use a 0.05 significance level.
---
#### Step 1: State the Null and Alternative Hypotheses
Select the correct null and alternative hypotheses for the test:
**A.** \( H_0: \mu = 0.51 \)
\[ H_a: \mu < 0.51 \]
**B.** (Correct)
\[ H_0: \mu = 0.51 \]
\[ H_a: \mu > 0.51 \]
**C.**
\[ H_0: \mu \neq 0.51 \]
\[ H_a: \mu = 0.51 \]
**D.**
\[ H_0: \mu = 0.51 \]
\[ H_a: \mu \neq 0.51 \]
---
#### Step 2: Calculate the Z-Score
Using the provided data:
- Sample Mean (\( \bar{x} \)) = 0.59
- Population Mean (\( \mu \)) = 0.51
- Standard Deviation (\( \sigma \)) = 0.18
- Sample Size (\( n \)) = 36
First, find the Standard Error (SE):
\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.18}{\sqrt{36}} = \frac{0.18}{6} = 0.03 \]
Then, calculate the Z-score:
\[ Z = \frac{\bar{x} - \mu}{SE} = \frac{0.59 - 0.51}{0.03} = \frac{0.08}{0.03} = 2.67 \]
So, the Z-score is:
\[ Z = \boxed{2.67} \]
*(Round to two decimal places as needed.)*
---
This Z-score can be used in further steps to determine the corresponding p-value, and to conclude whether there is sufficient evidence to reject the null hypothesis in favor of
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