Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.
-Independent samples from two different populations yield the following data. $\overline { x _ { 1 } } = 383 , \overline { x _ { 2 } } = 448$, s1 $= 44$, s2 $= 18$. The sample size is 177 for both samples. Find the 85 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$.
A) $- 72

Question

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.
-Independent samples from two different populations yield the following data. $\overline { x _ { 1 } } = 383 , \overline { x _ { 2 } } = 448$, s1 $= 44$, s2 $= 18$. The sample size is 177 for both samples. Find the 85 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$.
A) $- 72 < \mu _ { 1 } - \mu _ { 2 } < - 58$
B) $- 66 < \mu _ { 1 } - \mu _ { 2 } < - 64$
C) $- 79 < \mu _ { 1 } - \mu _ { 2 } < - 51$
D) $- 71 < \mu _ { 1 } - \mu _ { 2 } < - 59$

Quizplus · Accepted Answer

The confidence interval for the difference between two means, $\mu_1 - \mu_2$, can be calculated using the formula: $\overline{x}_1 - \overline{x}_2 \pm z \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $\overline{x}_1$ and $\overline{x}_2$ are the sample means, $s_1$ and $s_2$ are the sample standard deviations, $n_1$ and $n_2$ are the sample sizes, and $z$ is the z-score corresponding to the desired confidence level. Given $\overline{x}_1 = 383$, $\overline{x}_2 = 448$, $s_1 = 44$, $s_2 = 18$, and $n_1 = n_2 = 177$, and for an 85% confidence interval (which corresponds to a z-score of approximately 1.44), the calculation yields a confidence interval of approximately $-72$ to $-58$, making choice A correct.

Construct the Indicated Confidence Interval for the Difference Between the Two