Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=210​, x =26.9 ​hg, s=6.1 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 25.8 hg <ul <27.4 hg with only 16 sample​ values, x =26.6 ​hg, and s =1.9 ​hg?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.9

sample standard deviation = s = 6.1

sample size = n = 210

Degrees of freedom = df = n - 1 = 210 - 1 = 209

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t_0.05,209 = 1.652

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

= 1.652 * (6.1 / 210)

Margin of error = E = 0.7

The 99% confidence interval estimate of the population mean is,

   - E < < + E

26.9 - 0.7 < < 26.9 + 0.7

( 26.2 < < 27.6 )