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Chapter 12: Q.12.21 (page 491)

Distribution 0.2,0.1,0.1,0.3,0.3.

observed frequencies 9,7,1,12,21..

Significant level α=0.10.

Short Answer

Expert verified

The variable has given distribution.0.2,0.1,0.1,0.3,0.3

Step by step solution

01

Given Information

Distribution 0.2,0.1,0.1,0.3,0.3.

observed frequencies 9,7,1,12,21..

Significant level α=0.10.

02

Explanation

To find the goodness fit test,

No. of. Sample size =9+7+1+12+21.

Observed frequencies9711221Relative frequenciesp0.20.10.10.30.3Expected frequenciesnp105515v(obs-exp)2exp0.10.83.20.62.4χ2=∑(obs-exp)2exp=7.1

Degrees of freedom,

=k-1

=5-1

=4

03

Explanation

The critical value, with 4dfis χ20,10=7.779

χ2=7.1<χ20,10=7.779

Because it does not comes in the rejection region. To accept the Null hypothesis H0.

H0has distribution in the given problem.

Therefore, the variable has given distribution.

The pvalue is: 0.13060.1306

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Most popular questions from this chapter

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.

Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.

type of employer and response

Studies have shown that a positive association exists between educational level and annual salary; in other words, people with more education tend to make more money.
a. Does this finding mean that more education causes a person to make more money? Explain your answer.
b. Do you think there is a casual relationship between educational level and annual salary? Explain your answer.

For a χ2-curve with df=10, determine

a. χ0.052

b.χ0.025

Step 1 of Procedure 13.2 gives generic statements for the null and alternative hypotheses of a chi-square independence test. Use the terms statistically dependent and statistically independent, introduced on page 496, to restate those hypotheses.
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