Question

A simple random sample of checks were categorized based on the number of cents on the written check and recorded below.

Cents Category   0¢-24¢   25¢-49¢   50¢-74¢   75¢-99¢
Frequency          58        37        28        17

Use the critical value method and a 1% significance level to test the claim that the frequencies of the cents categories of checks fit the uniform distribution.

Calculate the expected frequency of the 25¢-49¢ category.

Answer 1

null hypothesis:Ho:Cents categories are uniformly distributed.

Alternate hypothesis:Ho:Cents categories are not uniformly distributed.

degree of freedom =categories-1=			3
for 0.01 level and 3 df :crtiical value X2 =			11.3449
Decision rule: reject Ho if value of test statistic X2>11.345

expected frequency of the 25¢-49¢ category =Np=140*0.25 =35

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
girls	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
0C-24C	0.25	58	35.00		15.114
25C-49C	0.25	37	35.00		0.114
50C-74C	0.25	28	35.00		1.400
75C-99C	0.25	17	35.00		9.257
total	1	140	140		25.8857
test statistic X2 =		25.886

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that the frequencies of the cents categories of checks does not fit the uniform distribution.