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Chapter 12: Q. 12.22 (page 491)

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 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: \(45, 39, 16\)

Significance level: \(=0.01\)

Short Answer

Expert verified

The variable has given distribution.

Step by step solution

01

Step 1. Given information

Distribution: \(0.5, 0.3, 0.2\)

Observed frequencies: \(45, 39, 16\)

Significance level: \(=0.01\)

02

Step 2. Calculation

Consider goodness of fit test

The sample size

\(n=45+39+16\)

\(=100\)

Observed frequencies

\(45\)

\(39\)

\(16\)

Relative frequencies


\(0.5\)

\(0.3\)

\(0.2\)

Expected frequencies

\(50\)

\(30\)

\(20\)

\(\frac{(obs-exp)^{2}}{exp}

\(0.5\)

\(2.9\)

\(0.8\)

\(\chi^{2}=\sum \frac{(obs-exp)^{2}}{exp}=4.2\)

The degrees of freedom of given data

\(=k-1\)

\(=3-1\)

\(=2\)

The critical value, with \(2df\) is \(\chi ^{2}_{0.01}=9.210\)

\(\chi ^{2}=4.2<\chi ^{2}_{0.05}=9.210\)

Because, it does not come in rejection region. So we accept the Null hypothesis.

Hence, the variable has given specified region.

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Most popular questions from this chapter

Variegated Plants. Arabidopsis is a genus of flowering plants related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article "The Balance between Protein Synthesis and Degradation in Chloroplasts Determines Leaf Variegation in Arabidopsis yellow variegated Mutants" (The Plant Cell, Vol. 19, No. 4, pp. 1313-1328). In a second-generation cross of variegated plants, 216 were variegated and 84 were normal. Genetics predicts that 75% of crossed variegated plants would be variegated and 25% would be normal. At the 10% significance level, do the data provide sufficient evidence to conclude that the second generation of crossed variegated plants does not follow the genetic predictions?

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is m⋅n.

12.69 four and five

For a χ2-curve with df=4, determine

a. χ0.0052

b.χ0.012

How do you identify different chi-square distributions?

In each of Exercises 12.11-12.16, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fir text and the sample size. In each case, decide whether Assumptions 1 and 2 for using that text are satisfied.

Sample size : n= 50.

Relative frequencies: 0.22 , 0.21 , 0.25 , 0.30 , 0.02.
See all solutions

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