Question

he sample data below have been collected based on a simple random sample from a normally distributed population. Complete parts a and b.

7

5

0

7

6

5

9

8

9

3

a. Compute a 90​% confidence interval estimate for the population mean. The 90​% confidence interval for the population mean is from ______ to _________ (Round to two decimal places as needed. Use ascending​ order.)

b. Show what the impact would be if the confidence level is increased to 95​%.

Discuss why this occurs. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Round to two decimal places as needed. Use ascending​ order.)

A.The 95​% confidence interval is from _______ to _______​, which is narrower than the interval in part a. This is because the margin of error is greater for a higher confidence level.

B.The 95​% confidence interval is from ______ to ______ which is wider than the interval in part a. This is because the margin of error is greater for a smaller confidence level..

C.The 95​% confidence interval is from _____ to ______ which is wider than the interval in part a. This is because the margin of error is greater for a higher confidence level.

D.The 95​% confidence interval is from ____ to _____ which is narrower than the interval in part a. This is because the margin of error is greater for a smaller confidence level.

Answer 1

a(

sample mean 'x̄=		5.90
sample size    n=		10
std deviation s=		2.807
std error ='sx=s/√n=2.807/√10=		0.888

for 90% CI; and 9 df, critical t=		1.833	from excel: t.inv(0.95,9)
margin of error E=t*std error                            =		1.627
lower bound=sample mean-E =		4.273
Upper bound=sample mean+E=		7.527
from above 90% confidence interval for population mean =from 4.27 to 7.53

b)

C.The 95​% confidence interval is from 3.89 to 7.91 which is wider than the interval in part a. This is because the margin of error is greater for a higher confidence level.