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

0.100

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	33	21	24	22

Answer 1

The four categories are equally likely. So, expected proportion =1/4 = 0.25

The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
0-24	33	100*0.25=25	(33-25)2/25 = 2.56
25-49	21	100*0.25=25	(21-25)2/25 = 0.64
50-74	24	100*0.25=25	(24-25)2/25 = 0.04
75-99	22	100*0.25=25	(22-25)2/25 = 0.36
Sum =	100	100	3.6

Null and Alternative Hypotheses

H0​:p1​=0.25,p2​=0.25,p3​=0.25,p4​=0.25

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

Test Statistics:

χ² = ∑ ((fo-fe)²/fe) = 2.56+0.64+0.04+0.36 = 3.6

df = 4-1 =3

Critical value:

χ²α = CHISQ.INV.RT(0.10, 3) = 6.251

p-value:

p-value = CHISQ.DIST.RT(3.6, 3) = 0.3080

Conclusion:

p-value > α, Do not reject the null hypothesis.

There is NOT enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the 0.10 significance level.