Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=231​, x overbar=31.2 ​hg, s=6.9 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 29.8hg < u< 33.4 hg with only 12 sample​ values, x overbar=31.6 ​hg, and s=2.8 ​hg?

A. What is the confidence interval for the population mean μ​? ____ hg < ​​​μ​ < ____ hg (Round to one decimal place as​ needed.)

B. 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

Given the sample size and sample mean , sample standard deviation .

A)The   two sided confidence interval for population mean based on the sample data is

We use t-distribution (although we know for large sample size, t-distribution converges to z-distribution), since population standard deviation is not known.

B) We an see that the means are contained in both the confidence intervals. Correct choice is

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