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.

Q: Expert Answer

a. To determine Perform χ 2 goodness fit test using p -value approach at α = 0.01 . Explanation 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: H 0 : p A = 0.40 , p B = 0.40 and p C = 0.20 . Alternative hypothesis: H a : The population proportions are not p A = 0.40 , p B = 0.40 and p C = 0.20 . Observed frequency for category A is obtained as f 1 = 60 with probability of 0.40, the observed frequency for category B is obtained as f 2 = 120 with probability of 0.40 and the observed frequency for category C is obtained as f 3 = 20 with probability of 0.20. The total sample size is 200. The expected frequency for category A is, e 1 = 200 ( 0.40 ) = 80 The expected frequency for category B is, e 2 = 200 ( 0.40 ) = 80 The expected frequency for category C is, e 3 = 200 ( 0.20 ) = 40 The formula for chi-square test statistic is given as, χ 2 = ∑ i = 1 k ( f i − e i ) 2 e i where f i is the observed frequency for category i , e i is the expected frequency for category i and k is the number of category b. To determine Perform a χ 2 goodness fit test using critical value approach at α = 0.01 .

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David R. Anderson + 4 others

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Essentials Of Statistics For Busin...

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David R. Anderson + 4 others

Publisher: South-Western College Pub

ISBN: 9780357045435

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Answer 5

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=0.40 and pC=0.20.

Alternative hypothesis:

Ha:The population proportions are not pA=0.40,pB=0.40 and 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(fi−ei)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

Answer 6

b.

To determine

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

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