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

Answer:

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 )

Step-by-step 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

= $t_{0.05/2} ,_{250-1} ( \frac{s}{\sqrt{n} } )$ ( 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 = $t_{0.05/2} ,_{19-1} ( \frac{s}{\sqrt{n} } )$ = 2.45 * ( 2.6 / 4.36 )  = 1.46

confidence interval

= ( 33.2 - 1.46 , 33.2 + 1.46 )

= ( 31.74 ,  34.66 )