e construct a confidence interval for the difference between two population means p, -, use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both n 2 30 and ny 2 30 Also, the samples must be randomly selected and independent The descriptive statistics for the annual salaries from a random sample of microbiologists from two regions are shown below. Construct a 95% confidence interval for the difference between the mean annual salaries *S108,920, n, = 40, and o, = $8550, = $85,300, n=43, and o, S8555 Complete the 95% confidence interval for u -p below. (Round to the nearest dollar as needed)
e construct a confidence interval for the difference between two population means p, -, use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both n 2 30 and ny 2 30 Also, the samples must be randomly selected and independent The descriptive statistics for the annual salaries from a random sample of microbiologists from two regions are shown below. Construct a 95% confidence interval for the difference between the mean annual salaries *S108,920, n, = 40, and o, = $8550, = $85,300, n=43, and o, S8555 Complete the 95% confidence interval for u -p below. (Round to the nearest dollar as needed)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![To construct a confidence interval for the difference between two population means \( \mu_1 - \mu_2 \), use the formula below when both population standard deviations are known, and either both populations are normally distributed or both \( n_1 > 30 \) and \( n_2 > 30 \). Also, the samples must be randomly selected and independent.
\[
(\overline{x}_1 - \overline{x}_2) - z \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} < \mu_1 - \mu_2 < (\overline{x}_1 - \overline{x}_2) + z \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}
\]
The descriptive statistics for the mean annual salaries from a random sample of microbiologists from two regions are shown below. Construct a 95% confidence interval for the difference between the mean annual salaries.
Region 1: \( \overline{x}_1 = \$100,920 \), \( n_1 = 40 \), and \( \sigma = \$8,550 \).
Region 2: \( \overline{x}_2 = \$98,300 \), \( n_2 = 43 \), and \( \sigma = \$8,565 \).
Complete the 95% confidence interval for \( \mu_1 - \mu_2 \) below.
\[
< \mu_1 - \mu_2 <
\]
(Round to the nearest dollar as needed.)
Enter your answer in each of the answer boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d4c8cb-af63-459c-8cdf-c777fdfe530a%2F7db7b507-e8e4-45a5-aefb-1ca2dea7299b%2Fp9a72yk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To construct a confidence interval for the difference between two population means \( \mu_1 - \mu_2 \), use the formula below when both population standard deviations are known, and either both populations are normally distributed or both \( n_1 > 30 \) and \( n_2 > 30 \). Also, the samples must be randomly selected and independent.
\[
(\overline{x}_1 - \overline{x}_2) - z \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} < \mu_1 - \mu_2 < (\overline{x}_1 - \overline{x}_2) + z \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}
\]
The descriptive statistics for the mean annual salaries from a random sample of microbiologists from two regions are shown below. Construct a 95% confidence interval for the difference between the mean annual salaries.
Region 1: \( \overline{x}_1 = \$100,920 \), \( n_1 = 40 \), and \( \sigma = \$8,550 \).
Region 2: \( \overline{x}_2 = \$98,300 \), \( n_2 = 43 \), and \( \sigma = \$8,565 \).
Complete the 95% confidence interval for \( \mu_1 - \mu_2 \) below.
\[
< \mu_1 - \mu_2 <
\]
(Round to the nearest dollar as needed.)
Enter your answer in each of the answer boxes.
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