Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=159​, x=32.1 ​hg, s=6.8hg. Construct a confidence interval estimate of the mean. Use a 99​%

confidence level. Are these results very different from the confidence interval 30.8 hg <μ<34.4 hg with only 18 sample​ values, x=32.6hg, and s=2.6hg?

Answer 1

Solution :

Given that n = 159 , x = 32.1 , and s = 6.8

=> df = n - 1 = 158

=> For 99% confidence interval , t = 2.6073

=> A 99% confidence interval of the mean is

=> x +/- t*s/sqrt(n)
  
=> 32.1 +/- 2.6073*6.8/sqrt(159)

=> (30.6939 , 33.5061)

=> 30.7 < μ < 33.5

Given that n = 18 , x = 32.6 , and s = 2.6

=> df = n - 1 = 17

=> For 99% confidence interval , t = 2.8982

=> A 99% confidence interval of the mean is

=> x +/- t*s/sqrt(n)

=> 32.6 +/- 2.8982*2.6/sqrt(18)

=> (30.8239 , 34.3761)

=> 30.8 < μ < 34.4

=> No, because the confidence interval limits are similar