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 51 18 13 18

Click here to view the chi-square distribution table. LOADING...

The test statistic is nothing. ​(Round to three decimal places as​ needed.)

The critical value is nothing. ​(Round to three decimal places as​ needed.)

State the conclusion. ▼ Do not reject Reject Upper H 0. There ▼ is is not sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results ▼ do not appear appear to support the expectation that the frequency for the first category is disproportionately high.

Answer 1

let us consider

H0 : the four categories are equally likely

H1:  the four categories are not equally likely

cents portion of check	number (O)	expected(E)	(O-E)2	(O-E)2/E
0-24	51	36.5	210.25	5.760
25-49	18	36.5	342.25	9.377
50-74	13	36.5	552.25	15.130
75-99	18	36.5	342.25	9.377
	100

Mean where x is the mid values and f is frequency

=3650/100

=36.5

5.760 + 9.377 + 15.130 + 9.377 = 39.644.

The test statistic is 39.644.

The critical value at 0.10 with 4-1 degree of freedom is 6.251

since test statistic is greater than critical value so we reject the null hypothesis

There is sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results do not  appear to support the expectation that the frequency for the first category is disproportionately high.