Question

Here are summary statistics for randomly selected weights of newborn​ girls: n​=250, x_=32.9 ​hg, s= 6.9 hg. Construct a confidence interval estimate of the mean. Use a ​95% confidence level. Are these results very different from the confidence interval 31.9 hg < μ < 34.5 hg with only 19 sample​ values, x_=33.2 ​hg, and s=2.6hg? What is the confidence interval for the population mean ​μ?

Answer 1

a) ( 31.92 < μ < 33.88 )

The confidence interval is not very different from the confidence interval given in the question

b) ( 31.74 , 34.66 )

Explanation:

n = 250

x ( mean ) = 32.9

std = 6.9

95% confidence interval

df = n - 1 = 250 - 1 = 249

a) construct confidence interval estimate

calculate for the margin of error

=
`t_(0.05/2) ,_(250-1) ( (s)/(√(n) ) )` ( using excel function: T.INV.2T(0.025,249) )

= 2.255 ( 6.9 / 15.81 )

= 0.98

Hence the confidence interval for the population

= ( x - 0.98 < μ < x + 0.98 )

= ( 31.92 < μ < 33.88 )

The confidence interval is not very different from the confidence interval given in the question

b) when n = 19

x = 33.2 and std = 2.6

margin of error =
`t_(0.05/2) ,_(19-1) ( (s)/(√(n) ) )` = 2.45 * ( 2.6 / 4.36 ) = 1.46

confidence interval

= ( 33.2 - 1.46 , 33.2 + 1.46 )

= ( 31.74 , 34.66 )