Question

Conduct the hypothesis test and provide the test​ statistic, critical value, and​ P-value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.10 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first​ category, but do the results support that​ expectation?

Cents portion of check: ​0-24, ​25-49, ​50-74, ​75-99

Number: 32, 24, 17, 27

Answer 1

Okay, this is a question of chi square test for goodness of fit.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

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

(2) Rejection Region

Based on the information provided, the significance level is α=0.10, the number of degrees of freedom is df=4−1=3, so then the rejection region for this test is R={χ2:χ2>6.251}.

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

The P-Value is 0.193486

(4) Decision about the null hypothesis

Since it is observed that χ2=4.72≤χc2​=6.251, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.10 significance level.

Also  The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first​ category, but the results DO NOT support that​ expectation.