Question

Conduct the hypothesis test and provide the test statistic and the critical​ value, and state the conclusion. A person randomly selected 100100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.100.10 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	5757	1919	1313	1111

1) The test statistic is

2)The critical value is

3

Answer 1

Q1) As we are testing the claim that all the four categories are equally likely, therefore the expected frequency for each of the 4 categories here would be computed as: 100*0.25 = 25

The chi square test statistic here is computed as:

Therefore 56 is the test statistic value here.

Q2) As we are testing here at 0.1 level of significance, for n - 1 = 3 degrees of freedom, we have from the chi square distribution tables:

Therefore,

Therefore 6.2514 is the critical value required here.