Question

Here are summary statistics for randomly selected weights of newborn​ girls: n equals 228​, x over bar equals 32.8 ​hg, s equals 6.9 hg. Construct a confidence interval estimate of the mean. Use a 99​% confidence level. Are these results very different from the confidence interval 30.7 hg less than mu less than 34.3 hg with only 20 sample​ values, x over bar equals 32.5 ​hg, and s equals 2.8 ​hg?

Answer 1

Since the sample is large (sample size of 30 or more), the central limit theorem tells us that the sampling distribution of the sample means is approximately normal.

Refer Standard normal table/Z-table or use excel function "=NORM.S.INV((1-0.005))" to find the Z-value.