Question

Here are summary statistics for randomly selected weights of newborn​ girls: n equals 175​, x over bar equals 27.7 ​hg, s equals7.9 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. 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

Solution :

Given that,

= 27.7

s = 7.9

n = 175

Degrees of freedom = df = n - 1 = 175 - 1 = 174

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,175 = 1.974

Margin of error = E = t_/2,df * (s /n)

= 1.974 * (7.9 / 175)

= 1.2

The 95% confidence interval estimate of the population mean is,

- E < < + E

27.7 - 1.2 < < 27.7 + 1.2

26.5 < < 28.9