Statistics Word Problem

Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value ​t a/2, ​(b) find the critical value z a/2​, or​ (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn​ girls: n​= 205, x bar = 31.8 ​hg, s= 7.8 hg. The confidence level is ​95%

Answer 1

Since out N=205, we have enough data to be able to assume it's approximately normal, this means that answer c is Not the right one. The piece that we're missing, unless you forgot to include it, is what value of the mean do we want to test (i.e. hypothesis test) for?

Without that information, all we can do is use what we know about the normal distribution, which is that 95% of the data are within 2 standard deviations for the mean. Since they want a 95% confidence interval, simply multiply s by 2:[7.8*2=15.6]. Next add & subtract that from the mean: (31.8-15.6)=16.2, and (31.8 +15.6)=47.4. We get a 95% Confidence Interval of (16.2, 47.4).