Attempts: Score: /5 3. The chi-square test for goodness of fit (no preference) -
ID: 3369937 • Letter: A
Question
Attempts: Score: /5 3. The chi-square test for goodness of fit (no preference) - Reaching a conclusion Aa Aa A chi-square hypoth possible categories distributed equally into all four categories with the following proportions: esis test for goodness of fit is conducted to determine if there is any preference among four in a population distribution. The no-preference null hypothesis states that the population is Category A B CD Proportion under Ho 25% 25% 25% 25% A random sample of n 300 observations is obtained from the population. The resulting observed frequencies and the corresponding expected frequencies associated with the null hypothesis are shown in the table be low. A B C D Observed frequency (fo) 96 73 66 65 Expected frequency (fe) 75 75 75 75 Category The chi-square test statistic for the above frequency data is x? 8.34 (see explanation for details). Use the Distributions tool to answer the questions below Chi-Square Distribution Degrees of Freedom 3 01 2 3 4 5 6 7 8 9 10 11 12 There are df - degrees of freedom in this example. With a .01, the critical value is The value of the x2 test statistic is The null hypothesis than the critical value. rejected You conclude there are significant differences among the four categories.Explanation / Answer
Degree of freedom= r-1
= 4-1
=3
Alpha =0.01,the critical value is 11.34487
Since the test statistics value is less than the critical value so we do not have sufficient evidence to reject the null hypothesis.
The null hypothesis is not rejected.Therefore we cannotconclude that there are significant differences between the proportions.
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