Question

A die is suspected of being biased. It is rolled 24 times with the following results:

Outcome	1	2	3	4	5	6	Total
Outcome Probability	1/6	1/6	1/6	1/6	1/6	1/6	1
Expected Frequency	A	B	C	D	E	F	24
Observed Frequency	8	4	1	8	3	0	24

1) Conduct a significance test at a significant level of 5% to see if the die is biased.

A die is not biased if the probability of each of the outcomes is equal to each other.

A die is biased if the probability of each of the outcomes is not equal to each other.

2)The numerical value of A is:

Enter answer as an integer or a decimal rounded to 3 places if appropriate.

3) The Null Hypothesis is: a The die is biased.

a) The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are not equal. (There is a statistical difference between the expected frequency and the observed frequency.)

b) The die is not biased. The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are equal. (There is no statistical difference between the expected frequency and the observed frequency.)

Enter answer by selecting the appropriate letter.

4) The Alternate Hypothesis is:

a) The die is biased. The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are not equal. (There is a statistical difference between the expected frequency and the observed frequency.)

b) The die is not biased. The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are equal. (There is no statistical difference between the expected frequency and the observed frequency.)

Enter answer by selecting the appropriate letter.

5) The appropriate distribution for performing the Hypothesis Test is:

a) Uniform Distribution

b) Normal Distribution

c) t Distribution

d) Chi Square Distribution

e) F Distribution

Enter answer by selecting the appropriate letter.

6) The numerical value of the Test Statistic is:

Enter the answer rounded to 1 decimal places.

7)The Pvalue is:

Enter the answer rounded to 3 decimal places. Do not enter answer as a percent.

8)Based upon the analysis of the data:

a) The null hypothesis is not rejected because the Pvalue is larger than the significance level of the test. (The test statistic is less than the critical value.)

b) The null hypothesis is rejected because the Pvalue is less than the significance level of the test. (The test statistic is greater than the critical value.)

Enter answer by selecting the appropriate letter.

Answer 1

A die is suspected of being biased. It is rolled 24 times with the following results:

Outcome	1	2	3	4	5	6	Total
Outcome Probability	1/6	1/6	1/6	1/6	1/6	1/6	1
Expected Frequency	A	B	C	D	E	F	24
Observed Frequency	8	4	1	8	3	0	24

1) Conduct a significance test at a significant level of 5% to see if the die is biased.

A die is not biased if the probability of each of the outcomes is equal to each other.

A die is biased if the probability of each of the outcomes is not equal to each other.

2)The numerical value of A is: 4

Enter answer as an integer or a decimal rounded to 3 places if appropriate.

Outcome	1	2	3	4	5	6	Total
Outcome Probability	1/6	1/6	1/6	1/6	1/6	1/6	1
Expected Frequency	4	4	4	4	4	4	24
Observed Frequency	8	4	1	8	3	0	24

3) The Null Hypothesis is:

The die is not biased. The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are equal. (There is no statistical difference between the expected frequency and the observed frequency.)

Enter answer by selecting the appropriate letter.

4) The Alternate Hypothesis is:

The die is biased. The probabilities for the outcomes (1, 2, 3, 4, 5, 6) are not equal. (There is a statistical difference between the expected frequency and the observed frequency.)

Enter answer by selecting the appropriate letter.

5) The appropriate distribution for performing the Hypothesis Test is:

d) Chi Square Distribution

Enter answer by selecting the appropriate letter.

6) The numerical value of the Test Statistic is: 14.5

Enter the answer rounded to 1 decimal places.

7)The Pvalue is: 0.013

Enter the answer rounded to 3 decimal places. Do not enter answer as a percent.

8)Based upon the analysis of the data:

b) The null hypothesis is rejected because the Pvalue is less than the significance level of the test. (The test statistic is greater than the critical value.)

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	8	4.000	4.000	4.000
	4	4.000	0.000	0.000
	1	4.000	-3.000	2.250
	8	4.000	4.000	4.000
	3	4.000	-1.000	0.250
	0	4.000	-4.000	4.000
	24	24.000	0.000	14.500
	14.50	chi-square
	5	df
	.0127	p-value