   # Test the following hypotheses by using the χ 2 goodness of fit test. H 0 : p A = .40, p B = .40, and p C = .20 H a : The population proportions are not p A = .40, p B = .40, and p C = .20 A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use α = .01 and test to see whether the proportions are as stated in H 0 . a. Use the p -value approach. b. Repeat the test using the critical value approach. ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435

#### Solutions

Chapter
Section ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435
Chapter 12.3, Problem 19E
Textbook Problem
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## Test the following hypotheses by using the χ2 goodness of fit test.H0: pA = .40, pB = .40, and pC = .20Ha: The population proportions are notpA = .40, pB = .40, and pC = .20A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use α = .01 and test to see whether the proportions are as stated in H0. a. Use the p-value approach. b. Repeat the test using the critical value approach.

a.

To determine

Perform χ2 goodness fit test using p-value approach at α=0.01.

### Explanation of Solution

Calculation:

A sample of size 200 yielded 60 in category A, 120 in category B and 20 in category C.

State the test hypotheses:

Null hypothesis:

H0:pA=0.40,pB=0.40and pC=0.20.

Alternative hypothesis:

Ha:The population proportions are not pA=0.40,pB=0.40and pC=0.20.

Observed frequency for category A is obtained as f1=60 with probability of 0.40, the observed frequency for category B is obtained as f2=120 with probability of 0.40 and the observed frequency for category C is obtained as f3=20 with probability of 0.20.

The total sample size is 200.

The expected frequency for category A is,

e1=200(0.40)=80

The expected frequency for category B is,

e2=200(0.40)=80

The expected frequency for category C is,

e3=200(0.20)=40

The formula for chi-square test statistic is given as,

χ2=i=1k(fiei)2ei where fi is the observed frequency for category i, ei is the expected frequency for category i and k is the number of category

b.

To determine

Perform a χ2 goodness fit test using critical value approach at α=0.01.

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