Question

Here are summary statistics for randomly selected weights of newborn​ girls: n = 165​, x = 29.2 , s = 6.8 Construct a confidence interval estimate of the mean. Use a 98 ​% confidence level. Are these results very different from the confidence interval 27.9 < mean < 30.7 with only 20 sample​ values, x = 29.3 hg, and s =2.5 hg? What is the confidence interval for the population mean​?

Answer 1

a) At 98% confidence interval the critical value is z^* = 2.33

The 98% confidence interval for population mean is

+/- z^* * s/

= 29.2 +/- 2.33 * 6.8/

= 29.2 +/- 1.23

= 27.97, 30.43

No, the results are not very different from the confidence interval 27.9 < mean < 30.7

b) At 98% confidence interval the critical value is t^* = 2.539

The 98% confidence interval for population mean is

+/- t^* * s/

= 29.3 +/- 2.539 * 2.5/

= 29.2 +/- 1.42

= 27.78, 30.62