Question

Here are summary statistics for randomly selected weights of newborn girls: nequals 219 , x overbar equals29.4 hg, sequals 7.5 hg. Construct a confidence interval estimate of the mean. Use a 99 % confidence level. Are these results very different from the confidence interval 26.9 hgless than muless than30.9 hg with only 20 sample values, x overbar equals28.9 hg, and sequals 3.2 hg?

What is the confidence interval for the population mean u?

______hg < u < _____ hg ​(Round to one decimal place as​ needed.)

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

.

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

B.

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

C.

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

D.

​No, because the confidence interval limits are similar.

Answer 1

Solution :

Given that,

= 29.4

s = 7.5

n = 219

Degrees of freedom = df = n - 1 = 219 - 1 = 218

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,218 =2.60

Margin of error = E = t_/2,df * (s /n)

= 2.60 * (7.5 / 219)

= 1.317

Margin of error =1.317

The 99% confidence interval estimate of the population mean is,

- E < < + E

29.4 - 1.317 < < 29.4+ 1.317

28.1 < < 30.7

(28.1 , 30.7 )

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