Question

Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.

A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 28, 27, 40, 38, 26, 41. Use a 0.01 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

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.

(1) __________ Ho . There (2) __________ sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes (3) __________ to be equally likely, so the loaded die (4) __________ to behave differently from a fair die.

(1) Do not reject
   Reject
(2) is
   is not
(3) appear
   do not appear
(4) does not appear
   appears

Answer 1

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	28	33.333	-5.333	0.853
	27	33.333	-6.333	1.203
	40	33.333	6.667	1.333
	38	33.333	4.667	0.653
	26	33.333	-7.333	1.613
	41	33.333	7.667	1.763
	200	200.000	0.000	7.420
	7.42	chi-square

test statistic is 7.420

critical value is 15.086

Do not reject , is not , appear , does not appear