Question

Here are summary statistics for randomly selected weights of newborn​ girls: nequals 250​, x overbar equals27.5 ​hg, s equals 7.1 hg. Construct a confidence interval estimate of the mean. Use a 95 ​% confidence level. Are these results very different from the confidence interval 26.6 hg less than muless than29.6 hg with only 17 sample​ values, x overbar equals 28.1 ​hg, and sequals 2.9 ​hg?

What is the confidence interval for the population mean u ​?

nothing hg less than u less than nothing hg ​(Round to one decimal place as​ needed.)

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

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

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 the confidence interval limits are not similar.

Answer 1

95% CI

One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
250	27.500	7.100	0.449	(26.6, 28.4)

μ: mean of Sample

One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
17	28.100	2.900	0.703	(26.6, 29.6)

μ: mean of Sample

The confidence interval for population mean = (26.6, 28.4) since we have taken a large sample size.

Increase in sample size decreases the margin of error that has been shown in the results. Lower the sample size more wider the confidence interval.

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

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