Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=168​, x =28.7 ​hg, s=6.1 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 27.2 hg<μ<29.4 hg with only 14 sample​ values, x =28.3 hg, and s=1.9 hg?

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 28.7

S = 6.1

n = 168

df = n – 1 = 167

Confidence level = 95%

Critical t value = 1.9743

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 28.7 ± 1.9743*6.1/sqrt(168)

Confidence interval = 28.7 ± 0.9291

Lower limit = 28.7 - 0.9291 = 27.8

Upper limit = 28.7 + 0.9291 =29.6

Confidence interval = (27.8, 29.6)

This interval is not very different from the confidence interval 27.2 hg<μ<29.4 hg, because lower and upper limits for both intervals are very close.