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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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Need C please
![**Text Transcription with Detailed Explanation:**
### Problem Statement
The question is whether shoppers at the mall spend less money on average the day after Thanksgiving compared to the day after Christmas. We have data from two groups:
- **Thanksgiving Shoppers:** 41 randomly surveyed shoppers with an average spending of $148 and a standard deviation of $38.
- **Christmas Shoppers:** 44 randomly surveyed shoppers with an average spending of $160 and a standard deviation of $42.
The significance level is set at \(\alpha = 0.01\).
For this study, the appropriate test is the **t-test for the difference between two independent population means**.
### Hypotheses
- **Null Hypothesis \(H_0\):**
\[
\mu_1 = \mu_2
\]
(The mean spending amount is equal for both groups.)
- **Alternative Hypothesis \(H_1\):**
\[
\mu_1 < \mu_2
\]
(The mean spending amount the day after Thanksgiving is less than the day after Christmas.)
### Testing Procedure
**a. Test Statistic**
The calculated test statistic is \(-1.383\), shown to three decimal places.
**b. P-value**
The p-value was not provided directly in the transcription but should match the context of the hypothesis test.
**c. Comparison**
The p-value is less than (or equal to) the significance level \(\alpha\).
**d. Conclusion**
Based on the comparison, we **fail to reject** the null hypothesis.
### Conclusion
The final conclusion, marked on the website, is:
"The results are statistically insignificant at \(\alpha = 0.01\); hence, there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend."
This analysis suggests that there is no statistically significant difference in the mean spending of shoppers the day after Thanksgiving compared to the day after Christmas at the given significance level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc260e632-e4e2-45c7-853f-2d07e95220d0%2Fb9be9d14-0d0c-4989-be70-a8d6e0e52db7%2Fjt1dq1p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription with Detailed Explanation:**
### Problem Statement
The question is whether shoppers at the mall spend less money on average the day after Thanksgiving compared to the day after Christmas. We have data from two groups:
- **Thanksgiving Shoppers:** 41 randomly surveyed shoppers with an average spending of $148 and a standard deviation of $38.
- **Christmas Shoppers:** 44 randomly surveyed shoppers with an average spending of $160 and a standard deviation of $42.
The significance level is set at \(\alpha = 0.01\).
For this study, the appropriate test is the **t-test for the difference between two independent population means**.
### Hypotheses
- **Null Hypothesis \(H_0\):**
\[
\mu_1 = \mu_2
\]
(The mean spending amount is equal for both groups.)
- **Alternative Hypothesis \(H_1\):**
\[
\mu_1 < \mu_2
\]
(The mean spending amount the day after Thanksgiving is less than the day after Christmas.)
### Testing Procedure
**a. Test Statistic**
The calculated test statistic is \(-1.383\), shown to three decimal places.
**b. P-value**
The p-value was not provided directly in the transcription but should match the context of the hypothesis test.
**c. Comparison**
The p-value is less than (or equal to) the significance level \(\alpha\).
**d. Conclusion**
Based on the comparison, we **fail to reject** the null hypothesis.
### Conclusion
The final conclusion, marked on the website, is:
"The results are statistically insignificant at \(\alpha = 0.01\); hence, there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is less than the population mean amount of money that day after Christmas shoppers spend."
This analysis suggests that there is no statistically significant difference in the mean spending of shoppers the day after Thanksgiving compared to the day after Christmas at the given significance level.
Expert Solution
Step 1: Given Information
Given that the value of the test statistic (t) = -1.383
sample size (n1) = 41
sample size (n2) = 44
Step by step
Solved in 3 steps with 2 images
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