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Chapter 12: Q.12.22 (page 491)

Distribution 0.5,0.3,0.2.

observed frequencies 45,39,16.

Significant levelα=0.01.

Short Answer

Expert verified

The variable has a given distribution0.5,0.3,0.2.

Step by step solution

01

Given Information

Given data:

Distribution 0.5,0.3,0.2.

observed frequencies 45,39,16.

Significant level α=0.01.

02

Explanation

To find the goodness fit test,

No. of. Sample size n=45+39+16

n=100.

Observed frequencies453916Relative frequenciesp0.50.30.2Expected frequenciesnp503020(obs-exp)2exp0.52.90.8χ2=∑(obs-exp)2exp=4.2

The degree of freedom,

=k-1

=3-1

=2

03

Explanation

The critical value, with 2dfis χ0,012=9.210

χ2=4.2<χ20,05=9.210

Because it isn't available in the rejection area. So the Null hypothesis is accepted.

As a result, the variable has a defined area.

The Pvalue is:0.010

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Most popular questions from this chapter

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution:0.5,0.3,0.2

Observed frequencies:147,115,88

Significance level=0.01

In each of the given Exercises, we have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x, and y, of a population. For each exercise, perform the following tasks.

a. Find the expected frequencies. Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic.

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

We stated earlier that, if two variables are not associated, ther eis no point in looking for a casual relationship. Why is that so?

In each of exercises 12.57-12.59, use the technology of your choice to solve the specified problems.

The Scottish Executive, Analytical Services Division Transport Statistics, compiles information on motorcycle accidents in Scotland. During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non built-up), are as presented on the WeissStats CD.
a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of day of the week within each type-of-road category and the marginal distribution of day of the week.
c. Determine the conditional distribution of type of road within each day of the week and the marginal distribution of type of road.
d. Does an association exist between the variables "day of the week" and "type of road" for these motorcycle accidents? Explain your answer.
Physician Specialty. According to the document Physician Specialty Data Book, published by the Association of American Medical Colleges, in 2010. 12.9%of active male physicians specialized in internal medicine and 15.3%of active female physicians specialized in internal medicine. Does an association exist between the variables "gender" and "specialty" for active physicians in 2010? Explain your answer.
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