Question

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

nequals=169169​,

x overbarxequals=27.627.6

​hg,

sequals=6.96.9

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

9090​%

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

26.526.5

hgless than<muμless than<28.928.9

hg with only

1616

sample​values,

x overbarxequals=27.727.7

​hg, and

sequals=2.72.7

​hg?

What is the confidence interval for the population mean

muμ​?

nothing

hgless than<muμless than<nothing

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

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

A.

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

B.

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

C.

​No, because the confidence interval limits are similar.

D.

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

Answer 1

sample mean, xbar = 27.6
sample standard deviation, s = 6.9
sample size, n = 169
degrees of freedom, n - 1 = 168

For 90% Confidence level, the t-value = 1.654
Here alpha = 0.1
alpha/2 = 0.05
t(alpha/2, df) = -1.654
t(1 - alpha/2, df) = 1.654

CI = (xbar - t*s/sqrt(n), xbar + t*s/sqrt(n))
CI = (27.6 - 1.654 * 6.9/sqrt(169) , 27.6 + 1.654 * 6.9/sqrt(169))
CI = (26.72 , 28.48)

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