Question

Here are summary statistics for randomly selected weights of newborn​ girls: nequals174​, x overbarequals30.8 ​hg, sequals7.5 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 28.5 hgless thanmuless than32.1 hg with only 15 sample​ values, x overbarequals30.3 ​hg, and sequals3.2 ​hg?

What is the confidence interval for the population mean mu​? 0 hgless thanmuless than 0 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 the confidence interval limits are 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

Solution :

degrees of freedom = n - 1 = 174 - 1 = 173

t/2,df = t0.025,173 = 1.974

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

= 1.974 * ( 7.5 / 174)

Margin of error = E = 1.1

The 95% confidence interval estimate of the population mean is,

- E < < + E

30.8 - 1.1 < < 30.8 + 1.1

29.7 hg < < 31.9 hg

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