http://lectures.mhhe.com/connect/0078020557/Table/table3.jpg - Table 3 Consider

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http://lectures.mhhe.com/connect/0078020557/Table/table3.jpg - Table 3

Consider a multinomial experiment with n = 220 and k = 4. The null hypothesis to be tested is H_0: p_1 = p_2 = p_3 = p_4 = 0.25.the observed frequencies resulting from the experiment are (Use Table 3): Choose the appropriate alternative hypothesis. All population proportions differ from 0.25. Not all population proportions are equal to 0.25. Calculate the critical value at the 5% significance level. (Round your answer to 3 decimal places.) Critical value _____ Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic _____ What is the conclusion to the hypothesis test? Reject H_0 since the value of the test statistic does not exceed the critical value. Do not reject H_0 since the value of the test statistic does not exceed the critical value. Do not reject H_0 since the value of the test statistic exceeds the critical value. Reject H_0 since the value of the test st

Explanation / Answer

a) not all population are equal to 0.25.

b) here degree of freedom =categories-1 =4-1=3

therefore critical value=7.815

c)applying chi square goodness of fit test:

from above test stat =8.25

d) reject Ho since the value of the test statistics exceeds the critical value.

observed Expected Chi square categories Probability O E=total*p =(O-E)^2/E 1 1/4 63.000 55.00 1.16 2 1/4 38.000 55.00 5.25 3 1/4 65.000 55.00 1.82 4 1/4 54.000 55.00 0.02 1 220 220 8.2545

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