Question

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

n=150,

x overbarxequals=31.7 ​hg,

s=6.4

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

95% confidence level. Are these results very different from the confidence interval

30.6

hgless than

hg with only

20

sample​ values,

x overbarxequals=31.6

​hg, and

sequals=2.1 ​hg?

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

hgless than

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

A.

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

B.

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

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 = 31.7
sample standard deviation, s = 6.4
sample size, n = 150
degrees of freedom, df = n - 1 = 149

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.976

ME = tc * s/sqrt(n)
ME = 1.976 * 6.4/sqrt(150)
ME = 1.0326

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (31.7 - 1.976 * 6.4/sqrt(150) , 31.7 + 1.976 * 6.4/sqrt(150))
CI = (30.7 , 32.7)

A.

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