Question

Here are summary statistics for randomly selected weights of newborn​ girls: n

equals 199​, x overbar x = 31.3 ​hg, s = 7.6 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 29.6 hg less than < mu μ < 32.8 hg with only 18 sample​ values, x overbar x = 31.2 ​hg, and s 3.3 ​hg?

What is the confidence interval for the population mean

mu

μ​?

Answer 1

Solution :

degrees of freedom = n - 1 = 199 - 1 = 198

t/2,df = t0.025,198 = 1.972

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

= 1.972 * ( 7.6 / 199)

Margin of error = E = 1.1

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

- E < < + E

31.3 - 1.1 < < 31.3 + 1.1

( 30.2 hg < < 32.4 hg )

Yes, because the confidence interval limits are not similar