Question

Here are summary statistics for randomly selected weights of newborn girls: n = 150 , x = 30.5 hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 90% confidence level. Are these results very different from the confidence interval 29.4hg < μ < 31.4 hg with only 19 sample values, x = 30.4 hg, and s = 2.5 hg?

What is the confidence interval for the population mean μ?

___________hg < μ < __________ hg (Round to one decimal place as needed.)

Are the results between the two confidence intervals very different?

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

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

C. No, because the confidence interval limits are similar.

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

Answer 1

a)
sample mean, xbar = 30.5
sample standard deviation, s = 6.7
sample size, n = 150
degrees of freedom, df = n - 1 = 149

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.655

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (30.5 - 1.655 * 6.7/sqrt(150) , 30.5 + 1.655 * 6.7/sqrt(150))
CI = (29.6 , 31.4)

29.6 < mu < 31.4

b)
B. No, because each confidence interval contains the mean of the other confidence interval.