Question

Here are summary statistics for randomly selected weights of newborn girls: n =211 , x =29.2hg, s=7.5 hg. Construct a confidence interval estimate of the mean. Use a 98 % confidence level. Are these results very different from the confidence interval 27.2hg <μ <32.2hg with only 12 sample values, x =29.7hg, and s=3.2 hg?

What is the confidence interval for the population mean μ ?

?hg < μ < ? hg (Round to one decimal place as needed

Are the results between the two confidence intervals very different?

A.

Yes, because the confidence interval limits are not similar.

B.

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

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

Answer:

Given,

To determine the confidence interval for the population mean μ

n = 211

x = 29.2

s = 7.5

Here significance level = 1 - 0.98

= 0.02

degree of difference = n - 1

= 211 - 1

= 210

Now critical value for 0.02 significance level and 210 degree of difference is t = 2.344

Standard error = s/sqrt(n)

substitute values

Standard error = 7.5/sqrt(211)

Standard error = 0.5163

Margin of error = t*standard error

substitute values

= 2.344*0.5163

= 1.21

Now lower limit = x - margin of error

substitute values

= 29.2 - 1.21

= 27.99

Upper limit = x + margin of error

= 29.2 + 1.21

= 30.41

27.99 < < 30.41

Here we can say that Yes it is due to that the confidence interval limits are not similar.

i.e., Option A