Question

onduct 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.)

Answer 1

Given data :

n=200

k=6=Number of categories

Hypothesis:

at least one Pi is not equal to 1/6

Test statistics:

Where Oi=Obsered frequecy

Ei=Expected Frequency

k=Number of categories

	Oi	Ei	Oi-Ei	(Oi-Ei)2	(Oi-Ei)2/ Ei
1	28	33.3333	-5.3333	28.4444	0.8533
2	27	33.3333	-6.3333	40.1111	1.2033
3	40	33.3333	6.6666	44.4444	1.3333
4	38	33.3333	4.6666	21.7778	0.6533
5	26	33.3333	-7.3333	53.7778	1.6133
6	41	33.3333	7.6667	58.7778	1.7633
					7.420

Degrees of freedom=k-1=5

Critical Value:

Critical value :is the value appering in the table for the specifies statistical test with what computed null hypothesis can be rejected

Chi-square critical value with significance level 0.01 with d.f =5 is given by

=15.086

Decision

Test statistics=7.420 < Critical valuw 15.086

We failed to reject H₀

There is not enough evidence to reject the null hypothesis and we have not sufficient eidence to conclude that the loaded die behave differently than a fair die