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Chapter 12: Q. 12.35 (page 493)

The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has c possible values. If the number of possible values is 2, that is, c=2, the chi-square goodness-of-fit test is equivalent to a procedure that you studied earlier.

a) Which procedure is that? Explain your answer.

b) Suppose that you want to perform a hypothesis test to decide whether the proportion of a population that has a specified attribute is different from p_0. Discuss the method for performing such a test if you use (1) the one-proportion z-test (page 463) or (2) the chi-square goodness-of-fit test.

Short Answer

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Ans:

(a) The chi-square suitability test provides a hypothesis test method for the distribution of variance with approximately c values. If the probable value of 2 is, i.e., c=2, the chi-square test of goodness-of-fit is equal to the process of one part of z.

(b) Suppose we want to do a hypothesis test to determine if the proportion of people with the specified attribute is different from, p0. We are doing a chi-square goodness-of-fit test.

Step by step solution

01

Step 1. Given information.

given,

The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has c possible values.

02

Step 2. (a)  Which procedure: 

The chi-square suitability test provides a hypothesis test method for the distribution of variance with approximately c values. If the probable value of 2 is, i.e., c=2, the chi-square test of goodness-of-fit is equal to the process of one part of z.

03

Step 3. (b)  Now,

Suppose we want to do a hypothesis test to determine if the proportion of people with the specified attribute is different from,p0. We are doing a chi-square goodness-of-fit test.

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Part (a): Use the two-portionsz-test to perform the required hypothesis test.

Part (b): Use the chi-square homogeneity test to perform the required hypothesis test.

Part (c): Compare your results in parts (a) and (b).

Part (d): Explain what principle is being illustrated.

In each case, decide whether Assumptions 1and 2for using chi-square goodness-of-fit test are satisfied.

Sample size: n=100.

Relative frequencies:0.65,0.30,0.05.

Fill in the blank: If a variable has only two possible values, the chi-square homogeneity test provides a procedure for comparing several population......................................
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