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You may need to use the appropriate appendix table or technology to answer this question. The makers of a soft drink want to identify the average age of its consumers. sample of 52 consumers was taken. The average age in the sample was 24 years with a standard deviation of 5 years. (Round your answers to three decimal places.) (a) Construct a 95% confidence interval for the true average age (in years) of the consumers. years to years (b) Construct an 80% confidence interval for the true average age (in years) of the consumers. years to years (c) Discuss why the 95% and 80% confidence intervals are different.

You may need to use the appropriate appendix table or technology to answer this question. The makers of a soft drink want to identify the average age of its consumers. sample of 52 consumers was taken. The average age in the sample was 24 years with a standard deviation of 5 years. (Round your answers to three decimal places.) (a) Construct a 95% confidence interval for the true average age (in years) of the consumers. years to years (b) Construct an 80% confidence interval for the true average age (in years) of the consumers. years to years (c) Discuss why the 95% and 80% confidence intervals are different.

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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ab K 21 You may need to use the appropriate appendix table or technology to answer this question. The makers of a soft drink want to identify the average age of its consumers. A sample of 52 consumers was taken. The average age in the sample was 24 years with a standard deviation of 5 years. (Round your answers to three decimal places.) esc (a) Construct a 95% confidence interval for the true average age (in years) of the consumers. years to years (b) Construct an 80% confidence interval for the true average age (in years) of the consumers. years to years (c) Discuss why the 95% and 80% confidence intervals are different. O Changing the confidence level or sample size while all else stays the same shifts the confidence interval left or right. 82°F Sunny Need Help? Read It Lo A O As the sample size decreases and all else stays the same, the confidence interval becomes narrower. As the confidence level decreases and all else stays the same, the confidence interval becomes narrower. O As the confidence level decreases and all else stays the same, the confidence interval becomes wider. O As the sample size decreases and all else stays the same, the confidence interval becomes wider. JE Z W S X # 3 D $ C 4 R F 40 % 5 V 16 4- T G 6 B 17 + Y & H fg 7 N fg 8 J hp DII Σ 200 to DDI K D L f12 insert V alt 6 ... prt sc C ctri delete 1 backspace pause home num lock 4x D end L enter 5:18 PM 9/18/2022 home pg up → 00
Transcribed Image Text:ab K 21 You may need to use the appropriate appendix table or technology to answer this question. The makers of a soft drink want to identify the average age of its consumers. A sample of 52 consumers was taken. The average age in the sample was 24 years with a standard deviation of 5 years. (Round your answers to three decimal places.) esc (a) Construct a 95% confidence interval for the true average age (in years) of the consumers. years to years (b) Construct an 80% confidence interval for the true average age (in years) of the consumers. years to years (c) Discuss why the 95% and 80% confidence intervals are different. O Changing the confidence level or sample size while all else stays the same shifts the confidence interval left or right. 82°F Sunny Need Help? Read It Lo A O As the sample size decreases and all else stays the same, the confidence interval becomes narrower. As the confidence level decreases and all else stays the same, the confidence interval becomes narrower. O As the confidence level decreases and all else stays the same, the confidence interval becomes wider. O As the sample size decreases and all else stays the same, the confidence interval becomes wider. JE Z W S X # 3 D $ C 4 R F 40 % 5 V 16 4- T G 6 B 17 + Y & H fg 7 N fg 8 J hp DII Σ 200 to DDI K D L f12 insert V alt 6 ... prt sc C ctri delete 1 backspace pause home num lock 4x D end L enter 5:18 PM 9/18/2022 home pg up → 00
Expert Solution
Step 1

Let μ and σ denote respectively the population mean and standard deviation of age of the consumers.

Given that n=52, x¯=24, s=5.

In this problem, σ is unknown. The population distribution is also unknown. The sample size is 52 which is sufficiently large (i.e. n≥30). So, a 100×(1-α)% confidence interval for μ is (x¯-E,x¯+E), where E=tα2;(n-1)×sn and α=1-confidence level.

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