MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.](https://content.bartleby.com/qna-images/question/4b6db2d9-4c09-49d2-b260-82ef02d33a50/a8aeb5aa-68fb-4a32-b177-0a77e8df1f68/lllhd5_processed.jpeg)
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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