Question

Conduct the hypothesis test and provide the test statistic and the critical​ 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 0.05 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 53 15 19 13

Answer 1

H0: Null Hypothesis: The four categories are equally likely

HA: Alternative Hypothesis: The four categories are not equally likely

The Test Statistic is got as follows:

Cents portion of check	Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
0.24	53	25	31.36
25 - 49	15	25	4
50 - 74	19	25	1.44
75 - 99	13	25	5.76
Total = =			42.56

= 0.05

ndf = 4 - 1 = 3

From Table, critical value of = 7.815

Since calculated value of = 42.56 is greater than critical value of = 7.815, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that the four categories are equally likely .