Question

3.

Here are summary statistics for randomly selected weights of newborn​ girls: n=188​, x=27.2 ​hg, s=6.7 hg. Construct a confidence interval estimate of the mean. Use a 99​% confidence level. Are these results very different from the confidence interval 24.9 hg<μ<28.7 hg with only 15 sample​ values, x=26.8 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.

​No, because the confidence interval limits are similar.

B.

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

C.

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

D.

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

Answer 1

Solution :

degrees of freedom = n - 1 = 188 - 187

t/2,df = t_0.005,187 = 2.602

Margin of error = E = t_/2,df * (s /n)

= 2.602 * ( 6.7 / 188)

Margin of error = E = 1.3

The 99% confidence interval estimate of the population mean is,

- E < < + E

27.2 - 1.3 < < 27.2 + 1.3

( 25.9 hg < < 28.5 hg )

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