dmerence beiween two population means 1 "P2. shown beloww when boih population deviations are khown, and elther boin populations are hormally distributed or boih n1 and n2 2 30. Also, the samples must be randomly selected and independent. (X, - X2) - Z.

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 shown below when both population standard deviations are known, and either both populations are normally distributed or both \( n_1 \geq 30 \) and \( n_2 \geq 30 \). Also, the samples must be randomly selected and independent.

\[
(\overline{x}_1 - \overline{x}_2) - z_c \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} < \mu_1 - \mu_2 < (\overline{x}_1 - \overline{x}_2) + z_c \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}
\]

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.

\[
\overline{x}_1 = \$108,570, \quad n_1 = 39, \quad \sigma_1 = \$8650; \quad \overline{x}_2 = \$85,690, \quad n_2 = 42, \quad \sigma_2 = \$8625
\]

Complete the 95% confidence interval for \( \mu_1 - \mu_2 \) below:

\[
\$[ \] < \mu_1 - \mu_2 < \$[ \]
\]

*(Round to the nearest dollar as needed.)*
Transcribed Image Text:To construct a confidence interval for the difference between two population means \( \mu_1 - \mu_2 \), use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both \( n_1 \geq 30 \) and \( n_2 \geq 30 \). Also, the samples must be randomly selected and independent. \[ (\overline{x}_1 - \overline{x}_2) - z_c \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} < \mu_1 - \mu_2 < (\overline{x}_1 - \overline{x}_2) + z_c \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} \] 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. \[ \overline{x}_1 = \$108,570, \quad n_1 = 39, \quad \sigma_1 = \$8650; \quad \overline{x}_2 = \$85,690, \quad n_2 = 42, \quad \sigma_2 = \$8625 \] Complete the 95% confidence interval for \( \mu_1 - \mu_2 \) below: \[ \$[ \] < \mu_1 - \mu_2 < \$[ \] \] *(Round to the nearest dollar as needed.)*
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