In a survey of 1000 people, mean amount of money they spend on buying Starbuck's coffee per month is $19.40. Use z= 1.96 and o =45 a. What is the margin of error for this study? b. Give an interval that is likely to contain the exact mean amount of money people spend on Starbucks.
In a survey of 1000 people, mean amount of money they spend on buying Starbuck's coffee per month is $19.40. Use z= 1.96 and o =45 a. What is the margin of error for this study? b. Give an interval that is likely to contain the exact mean amount of money people spend on Starbucks.
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 6: Statistical Study**
In a survey of 1,000 people, the mean amount of money they spend on buying Starbucks coffee per month is $19.40. Use \( z = 1.96 \) and \( \sigma = 0.45 \).
a. **What is the margin of error for this study?**
b. **Give an interval that is likely to contain the exact mean amount of money people spend on Starbucks.**
---
**Solution Explanation:**
To calculate the margin of error (ME), use the formula:
\[
ME = z \times \left(\frac{\sigma}{\sqrt{n}}\right)
\]
where:
- \( z = 1.96 \) (z-score for a 95% confidence level)
- \( \sigma = 0.45 \) (standard deviation)
- \( n = 1000 \) (sample size)
Once the ME is calculated, the confidence interval can be determined using:
\[
\text{Confidence Interval} = \text{mean} \pm ME
\]
Substitute the values into the formulas above to find the margin of error and the confidence interval for the study results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b6db2d9-4c09-49d2-b260-82ef02d33a50%2Fa8aeb5aa-68fb-4a32-b177-0a77e8df1f68%2Flllhd5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6: Statistical Study**
In a survey of 1,000 people, the mean amount of money they spend on buying Starbucks coffee per month is $19.40. Use \( z = 1.96 \) and \( \sigma = 0.45 \).
a. **What is the margin of error for this study?**
b. **Give an interval that is likely to contain the exact mean amount of money people spend on Starbucks.**
---
**Solution Explanation:**
To calculate the margin of error (ME), use the formula:
\[
ME = z \times \left(\frac{\sigma}{\sqrt{n}}\right)
\]
where:
- \( z = 1.96 \) (z-score for a 95% confidence level)
- \( \sigma = 0.45 \) (standard deviation)
- \( n = 1000 \) (sample size)
Once the ME is calculated, the confidence interval can be determined using:
\[
\text{Confidence Interval} = \text{mean} \pm ME
\]
Substitute the values into the formulas above to find the margin of error and the confidence interval for the study results.
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