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 31 20 2 9 20 Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion to support Ho. There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results frequency for the first category is disproportionately high Do not reject Reject

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)2/E
0-24	31	0.25	100 * 0.25 = 25	(31 - 25)2/25 = 1.44
25-49	20	0.25	100 * 0.25 = 25	(20 - 25)2/25 = 1
50-74	29	0.25	100 * 0.25 = 25	(29 - 25)2/25 = 0.64
75-99	20	0.25	100 * 0.25 = 25	(20 - 25)2/25 = 1
Total	100	1.00	100	4.0800

Test statistic:

χ² = ∑ ((O-E)²/E) = 4.08

df = n-1 = 3

Critical value:

χ²α = CHISQ.INV.RT(0.05, 3) = 7.815

Do not reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim.

The result does not support.