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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