Question

Here are summary statistics for randomly selected weights of newborn girls: n=174, x=31.9 hg, s=7.7 hg. Construct a confidence interval estimate of the mean. Use a 95% confidence level. Are these results very different from the confidence interval 30.4 hg< μ < 34.2 hg with only 19 sample values, x=32.3 hg, and s=3.3 hg?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31.9

sample standard deviation = s = 7.7

sample size = n = 174

Degrees of freedom = df = n - 1 = 174 - 1 = 173

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

t/2,df = 1.654

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

= 1.654* (7.7 / 174)

Margin of error = E = 1.0

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

  ± E

31.9  ± 1.0

(30.9 , 32.9)

Yes, because the confidence interval limits are not similar