Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=263​, x overbar =35.1hg, s=8.38.3 hg. Construct a confidence interval estimate of the mean. Use a 96​% confidence level. Are these results very different from the confidence interval 33.0 hg < μ < 35.8 hg with only 24 sample​ values, x overbar= 34.4 ​hg, and s=3.23.2 hg?

What is the confidence interval for the population mean μ?

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

Answer 1

The 96% confidence interval of the population mean is:

[, ], where, = 35.1, s = 8.3, n = 263

Thus, 96% C.I. = [35.1 - 1.0564, 35.1 + 1.0564] = [34.0436, 36.1564]

The above confidence interval is bit different from the one obtained using a sample size of 24. Since, the sample size increases in the above case, the confidence interval becomes more accurate and the width of the interval decreases.