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 0.10 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	3131	2121	2828	2020

The test stat is?

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
Category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
0-24	0.2500	31	25.00		1.4400
25-49	0.2500	21	25.00		0.6400
50-74	0.2500	28	25.00		0.3600
75-99	0.2500	20	25.00		1.0000
total	1.00	100	100		3.4400
test statistic X2=		3.440

degree of freedom =categories-1=			3
for 0.1 level and 3 df :crtiical value X2 =			6.251	from excel: chiinv(0.1,3)

fail to reject Ho , there is not sufficient evidence to conclude that the results support that​ expectation.