(a) Explanation The given data shows the 654 young women, where the mean x ¯ = 26.8 , and the standard deviation is σ = 7.5 and 90%, 95% and 99% confidence levels. Calculation: 90% confidence interval : Critical value : From the Table A: Standard Normal Cumulative Proportions, the critical value for the probability 0.90 is the value is z * = 1.64 . The 90% confidence interval formula is, Confidence interval = x ¯ ± z * σ n Substitute 26.8 for x ¯ , 7.5 for σ , 1.64 for z * and 654 for n in confidence interval. Confidence interval = 26.8 ± 1.64 7.5 654 = 26.8 ± 1.64 ( 0.2933 ) = 26.8 ± 0.4810 = ( 26.3190 , 27.2810 ) Thus, the 90% confidence interval for mean BMI ( μ ) is 26.3190 and 27.2810. 95% confidence interval : From the Table A: Standard Normal Cumulative Proportions, the critical value for the probability 0.95 is the value is 1.96. The 95% confidence interval formula is, Confidence interval = x ¯ ± z * σ n Substitute 26.8 for x ¯ , 7.5 for σ , 1.96 for z * and 654 for n in confidence interval (b) To determine To identify: The margin of error for the 90%, 95%, and 99% confidence To explain: How the increase in the confidence level changes the margin of error of a confidence interval when the sample size and population standard deviation remain the same.

The 90%, 95% 99% confidence intervals for the body mass index (BMI) μ .

EBK THE BASIC PRACTICE OF STATISTICS

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ISBN: 8220103935319

Author: Moore

Publisher: YUZU

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Question

Chapter 16.4, Problem 16.8AYK

(a)

To determine

To identify: The 90%, 95% 99% confidence intervals for the body mass index (BMI) μ.

(b)

To determine

To identify: The margin of error for the 90%, 95%, and 99% confidence

To explain: How the increase in the confidence level changes the margin of error of a confidence interval when the sample size and population standard deviation remain the same.

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