Question

Here are summary statistics for randomly selected weights of newborn​ girls:

n=161​,

x=28.1

​hg,

s=7.8

hg. Construct a confidence interval estimate of the mean. Use a

95​%

confidence level. Are these results very different from the confidence interval

25.9

hg<μ<29.5

hg with only

15

sample​ values,

x=27.7

​hg, and

s=3.3

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

μ​?

nothing

hg<μ<nothing

hg ​(Round to one decimal place as​ needed.)

Are the results between the two confidence intervals very​ different?

A.

​Yes, because one confidence interval does not contain the mean of the other confidence interval.

B.

​Yes, because the confidence interval limits are not similar.

C.

​No, because each confidence interval contains the mean of the other confidence interval.

D.

​No, because the confidence interval limits are similar.

Answer 1

Solution:

Note that, Population standard deviation() is unknown. So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 161 - 1 = 160

    =    =  _0.025,160 = 1.975

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

= 1.975 * (7.8 / 161)

= 1.2

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(28.1 - 1.2)   <   <  (28.1 + 1.2)

26.9 <   < 29.3

C. ​No, because each confidence interval contains the mean of the other confidence interval.