MATLAB: An Introduction with Applications
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![**Construct a 90% Confidence Interval for Mean Cholesterol Content Difference**
We aim to construct a 90% confidence interval for \( \mu_1 - \mu_2 \) using the sample statistics for the mean cholesterol content of hamburgers from two different fast food chains. The formula below is applied for populations that are approximately normal with unequal variances.
### Sample Statistics:
- For Fast Food Chain 1:
- Sample Mean (\( \bar{x}_1 \)): 116 mg
- Sample Standard Deviation (\( s_1 \)): 3.71 mg
- Sample Size (\( n_1 \)): 10
- For Fast Food Chain 2:
- Sample Mean (\( \bar{x}_2 \)): 62 mg
- Sample Standard Deviation (\( s_2 \)): 2.02 mg
- Sample Size (\( n_2 \)): 16
### Confidence Interval Formula When Variances Are Not Equal:
\[
(\bar{x}_1 - \bar{x}_2) - t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} < \mu_1 - \mu_2 < (\bar{x}_1 - \bar{x}_2) + t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\]
- Degrees of Freedom (d.f.) is the smaller of \( n_1 - 1 \) or \( n_2 - 1 \).
### Task:
Enter the endpoints of the interval:
\[ \text{[ ]} < \mu_1 - \mu_2 < \text{[ ]} \]
*(Round to the nearest integer as needed.)*](https://content.bartleby.com/qna-images/question/80780ac4-a408-4a93-b2bb-c6bfa58cb046/00084a7f-2223-459e-a2ce-28f09b1003d6/xrvl8qh_processed.jpeg)
Transcribed Image Text:**Construct a 90% Confidence Interval for Mean Cholesterol Content Difference**
We aim to construct a 90% confidence interval for \( \mu_1 - \mu_2 \) using the sample statistics for the mean cholesterol content of hamburgers from two different fast food chains. The formula below is applied for populations that are approximately normal with unequal variances.
### Sample Statistics:
- For Fast Food Chain 1:
- Sample Mean (\( \bar{x}_1 \)): 116 mg
- Sample Standard Deviation (\( s_1 \)): 3.71 mg
- Sample Size (\( n_1 \)): 10
- For Fast Food Chain 2:
- Sample Mean (\( \bar{x}_2 \)): 62 mg
- Sample Standard Deviation (\( s_2 \)): 2.02 mg
- Sample Size (\( n_2 \)): 16
### Confidence Interval Formula When Variances Are Not Equal:
\[
(\bar{x}_1 - \bar{x}_2) - t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} < \mu_1 - \mu_2 < (\bar{x}_1 - \bar{x}_2) + t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\]
- Degrees of Freedom (d.f.) is the smaller of \( n_1 - 1 \) or \( n_2 - 1 \).
### Task:
Enter the endpoints of the interval:
\[ \text{[ ]} < \mu_1 - \mu_2 < \text{[ ]} \]
*(Round to the nearest integer as needed.)*
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