Question

Here are summary statistics for randomly selected weights of newborn​ girls: n= 247​, x overbar = 28.7 ​hg, s = 6.4 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 26.9 hg < μ < 29.3 hg with only 15 sample​ values, x overbar = 28.1 ​hg, and s = 2.2 ​hg?

What is the confidence interval for the population mean μ​?

_ hg < μ < _ hg

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 28.7

sample standard deviation = s = 6.4

sample size = n = 247

Degrees of freedom = df = n - 1 = 247 - 1 = 246

b) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

t/2,df = 1.970

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

= 1.970* ( 6.4/ 247)

Margin of error = E = 0.8

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

  ± E  

28.7 ± 0.8

(27.9 , 29.5)

Yes, because the confidence interval limits are not similar