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Construct a confidence interval of a survey of annual earnings of Gateway students, using the following data: X= $54,000, s=$1,400. Size of the survey (n) is 50 students. a) Use the .98 confidence level. b) Change the confidence level to .95 and construct a confidence interval. c) Use the .95 confidence level and increase the "n" to 576 to find the confidence interval.

Construct a confidence interval of a survey of annual earnings of Gateway students, using the following data: X= $54,000, s=$1,400. Size of the survey (n) is 50 students. a) Use the .98 confidence level. b) Change the confidence level to .95 and construct a confidence interval. c) Use the .95 confidence level and increase the "n" to 576 to find the confidence interval.

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
Problem 1P
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Please round it to 4 decimal places and add the excel formulas as well.

### Constructing Confidence Intervals for Gateway Students' Annual Earnings In this exercise, you will learn to construct confidence intervals based on survey data. The survey targets the annual earnings of Gateway students and provides the following information: - **Sample Mean (\(\bar{X}\))**: $54,000 - **Sample Standard Deviation (s)**: $1,400 - **Sample Size (n)**: 50 students Follow the steps below to construct the confidence intervals: #### a) Confidence Interval using a 0.98 Confidence Level Calculate the confidence interval with a 98% confidence level. #### b) Confidence Interval with a 0.95 Confidence Level Adjust the confidence level to 95% and recompute the confidence interval. #### c) Confidence Interval at 0.95 Confidence Level with Increased Sample Size Keep the confidence level at 95%, but increase the sample size to 576. Then, find the updated confidence interval. Each confidence interval will provide a range that is likely to contain the true average annual earnings of Gateway students with varying degrees of certainty. Learning how different confidence levels and sample sizes impact the interval is crucial for statistical analysis.
Transcribed Image Text:### Constructing Confidence Intervals for Gateway Students' Annual Earnings In this exercise, you will learn to construct confidence intervals based on survey data. The survey targets the annual earnings of Gateway students and provides the following information: - **Sample Mean (\(\bar{X}\))**: $54,000 - **Sample Standard Deviation (s)**: $1,400 - **Sample Size (n)**: 50 students Follow the steps below to construct the confidence intervals: #### a) Confidence Interval using a 0.98 Confidence Level Calculate the confidence interval with a 98% confidence level. #### b) Confidence Interval with a 0.95 Confidence Level Adjust the confidence level to 95% and recompute the confidence interval. #### c) Confidence Interval at 0.95 Confidence Level with Increased Sample Size Keep the confidence level at 95%, but increase the sample size to 576. Then, find the updated confidence interval. Each confidence interval will provide a range that is likely to contain the true average annual earnings of Gateway students with varying degrees of certainty. Learning how different confidence levels and sample sizes impact the interval is crucial for statistical analysis.
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