Question

Here are summary statistics for randomly selected weights of newborn​ girls: n

equals 202​, x overbar x = 33.7 ​hg, s = 7.3 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 31.8 hg < mu < 34.6 hg with only 17 sample​ values, x overbar x = 33.2 ​hg, and s = 3.2 ​hg?

What is the confidence interval for the population mean

mu

μ​?

Are the results between the two confidence intervals very​ different?

A. ​No, because the confidence interval limits are similar.

B. Yes, because the confidence interval limits are not similar.

C. No, because each confidence interval contains the mean of the other confidence interval.

D. Yes, because one confidence interval does not contain the mean of the other confidence interval.

Answer 1

sample mean, xbar = 33.7
sample standard deviation, s = 7.3
sample size, n = 202
degrees of freedom, df = n - 1 = 201

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.652

ME = tc * s/sqrt(n)
ME = 1.652 * 7.3/sqrt(202)
ME = 0.849

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (33.7 - 1.652 * 7.3/sqrt(202) , 33.7 + 1.652 * 7.3/sqrt(202))
CI = (32.9 , 34.5)

B. Yes, because the confidence interval limits are not similar.