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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 *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.

**a.**

To determine

Perform *p*-value approach at

**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:*

*Alternative hypothesis:*

Observed frequency for category A is obtained as

The total sample size is 200.

The expected frequency for category A is,

The expected frequency for category B is,

The expected frequency for category C is,

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

*i*, *i* and *k* is the number of category

**b.**

To determine

Perform a

Essentials Of Statistics For Business & Economics

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