Construct a 95% confidence interval for u, - with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats X =71 mg, s, = 3.81 mg, n, = 15 X, = 50 mg, S,=2.02 mg, n2 = 20 Confidence .2 .2 interval when variances are not n2 equal d.f. is the smaller of n, -1 or n, -1 Enter the endpoints of the interval.

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Construct a 95% confidence interval for \( \mu_1 - \mu_2 \) with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances.

### Stats

- \( x_1 = 71 \) mg, \( s_1 = 3.81 \) mg, \( n_1 = 15 \)
- \( x_2 = 50 \) mg, \( s_2 = 2.02 \) mg, \( n_2 = 20 \)

### Confidence interval when variances are not equal

\[ (x_1 - x_2) - t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} < \mu_1 - \mu_2 < (x_1 - x_2) + t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \]

- d.f. is the smaller of \( n_1 - 1 \) or \( n_2 - 1 \)

### Enter the endpoints of the interval:

\[ < \mu_1 - \mu_2 < \] 

(Round to the nearest integer as needed.)
Transcribed Image Text:Construct a 95% confidence interval for \( \mu_1 - \mu_2 \) with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. ### Stats - \( x_1 = 71 \) mg, \( s_1 = 3.81 \) mg, \( n_1 = 15 \) - \( x_2 = 50 \) mg, \( s_2 = 2.02 \) mg, \( n_2 = 20 \) ### Confidence interval when variances are not equal \[ (x_1 - x_2) - t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} < \mu_1 - \mu_2 < (x_1 - x_2) + t_c \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \] - d.f. is the smaller of \( n_1 - 1 \) or \( n_2 - 1 \) ### Enter the endpoints of the interval: \[ < \mu_1 - \mu_2 < \] (Round to the nearest integer as needed.)
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