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Chapter 8: Q 62. (page 541)

Critical values What critical value t*from Table B should be used for a confidence interval for the population mean in each of the following situations?

a. A 90% confidence interval based on n=12 randomly selected observations

b. A 95% confidence interval from an SRS of 30 observations

c. A 99% confidence interval based on a random sample of size 58

Short Answer

Expert verified

a. The critical value is 1.796.

b. The critical value is 2.045.

c. The critical value is2.678.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that n=12

Confidence Level=0.90

02

Part (a) Step 2: Calculation

Degree of freedom is calculated as:

df=n-1=12-1=11

Level of Significance, a=0.10

EXCEL formula =TINV(0.1,11)gives

t11,a/2=1.796

The critical value is1.796

03

Part (b) Step 1: Given Information

It is given that n=30

Confidence Level=0.95

04

Part (b) Step 2: Calculation

Degree of freedom is calculated as:

df=n-1=30-1=29

Level of significance, a=0.05

EXCEL formula =TINV(0.05,29)gives

t11,a/2=1.045

The critical value is1.045

05

Part (c) Step 1: Given Information

It is given that n=58

Confidence Level0.999

06

Part (c) Step 2: Calculation

Degree of freedom is df=n-1=58-1=57

Level of Significance is a=0.01

EXCEL formula =TINV(0.01,57)gives

t11,a/2=2.678

The critical value is2.678

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