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Salaries of 33 college graduates who took a statistics course in college have a mean, x. of $60,100, Assuming a standard deviation, a, of $19.770, construct a 90% confidence interval for estimating the population mean u Click here to view at distribution table Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table, S

Salaries of 33 college graduates who took a statistics course in college have a mean, x. of $60,100, Assuming a standard deviation, a, of $19.770, construct a 90% confidence interval for estimating the population mean u Click here to view at distribution table Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table, S

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Constructing a 90% Confidence Interval for the Population Mean **Scenario:** The salaries of 33 college graduates who took a statistics course in college have a mean (\( \bar{x} \)) of \$60,100. The standard deviation (\( \sigma \)) is \$19,770. We want to construct a 90% confidence interval for estimating the population mean (\( \mu \)). **Instructions:** 1. **Distribution Table Links:** - Click the provided links to view the t-distribution and standard normal distribution tables, which will be used to find critical values: - [View t-distribution table](#) - [View Standard Normal Distribution Table Page 1](#) - [View Standard Normal Distribution Table Page 2](#) 2. **Finding the Confidence Interval:** - Compute the confidence interval using the formula for the confidence interval of the mean when the population standard deviation is known: \[ CI = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \] - Here, \( Z \) is the Z-score corresponding to the desired confidence level (90% in this case), \( \sigma \) is the standard deviation, and \( n \) is the sample size. **Input Box:** - Calculate the confidence interval and fill in the values for: \[ \$ [ \quad \text{Lower Limit} \quad ] < \mu < \$ [ \quad \text{Upper Limit} \quad ] \] - Round your results to the nearest integer as needed. Use these steps to determine the 90% confidence interval for the average salary of all such college graduates.
Transcribed Image Text:### Constructing a 90% Confidence Interval for the Population Mean **Scenario:** The salaries of 33 college graduates who took a statistics course in college have a mean (\( \bar{x} \)) of \$60,100. The standard deviation (\( \sigma \)) is \$19,770. We want to construct a 90% confidence interval for estimating the population mean (\( \mu \)). **Instructions:** 1. **Distribution Table Links:** - Click the provided links to view the t-distribution and standard normal distribution tables, which will be used to find critical values: - [View t-distribution table](#) - [View Standard Normal Distribution Table Page 1](#) - [View Standard Normal Distribution Table Page 2](#) 2. **Finding the Confidence Interval:** - Compute the confidence interval using the formula for the confidence interval of the mean when the population standard deviation is known: \[ CI = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \] - Here, \( Z \) is the Z-score corresponding to the desired confidence level (90% in this case), \( \sigma \) is the standard deviation, and \( n \) is the sample size. **Input Box:** - Calculate the confidence interval and fill in the values for: \[ \$ [ \quad \text{Lower Limit} \quad ] < \mu < \$ [ \quad \text{Upper Limit} \quad ] \] - Round your results to the nearest integer as needed. Use these steps to determine the 90% confidence interval for the average salary of all such college graduates.
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