Question

Here are summary statistics for randomly selected weights of newborn​ girls: n equals 226​, x over bar equals 32.1 ​hg, s equals 6.9 hg. Construct a confidence interval estimate of the mean. Use a 98​% confidence level. Are these results very different from the confidence interval 29.5 hg less than mu less than 33.5 hg with only 12 sample​ values, x over bar equals 31.5 ​hg, and equals 2.5 ​hg? What is the confidence interval for the population mean mu​? nothing hg less than mu less than nothing hg ​(Round to one decimal place as​ needed.)

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((1-0.01))" to find the Z-value.