Question

In: Statistics and Probability

I need to set up and run a goodness of fit test. I am trying to...

I need to set up and run a goodness of fit test. I am trying to learn more about the type of novels that people prefer to read.

Please include null and alternative hypotheses. Show all work and please explain if you use any excel tests.

Total number of responses is 30.

Romance: 18

Sci - Fi: 7

Fiction: 5

Solutions

Expert Solution

Here the observation table is

Categories Observed(Oi) Expected(Ei) (Oi-Ei)2/Ei
Romance 18 30*1/3=10 (18-10)2/10 = 6.4
Sci-Fi 7 30*1/3=10 (7-10)2/10 = 0.9
Fiction 5 30*1/3=10 (5-10)2/10 = 2.5
Sum = 30 30 9.8

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0: The types of novels follow discrete uniform distribution.

v/s

Ha: The types of novels does not follow discrete uniform distribution.

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = 3 - 1 = 2, so then the rejection region for this test is

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that , it is then concluded that the null hypothesis is rejected.

(5) Conclusion

There is not enough evidence to claim that the types of novels follow discrete uniform distribution at α=0.05 significance level.


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