Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=187​, x =30.8 ​hg, s=7.9 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 29.0 hg-mu-t32.4 hg with only 14 sample​ values, x=30.7 ​hg, and s=3.6 ​hg

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 30.8 hg

sample standard deviation = s = 7.9 hg

sample size = n = 187

Degrees of freedom = df = n - 1 = 187 - 1 = 186

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t_{0.05, 186} = 1.653

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

= 1.653 * ( 7.9/ 187)

Margin of error = E = 1.0

The 90% confidence interval estimate of the population mean is,

- E < < + E

30.8 - 1.0 < < 30.8 + 1.0

(29.8 < < 31.8)