A gambler complained about dice They seemed to be loaded The

A gambler complained about dice. They seemed to be loaded! The dice were taken off of the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded.

Outcome

1

2

3

4

5

6

Observed Frequency

62

45

63

32

47

51

Assuming the null hypothesis is that the observed frequency distributions are the same and the sample ² = 13.44, then at the 1% level of significance do we accept or reject the null hypothesis?

Select one:

A. Reject null hypothesis

B. Do Not Reject null hypothesis

C. Not enough information

D. None of the above

Outcome	1	2	3	4	5	6
Observed Frequency	62	45	63	32	47	51

Solution

A gambler complained about dice. They seemed to be loaded! The dice were taken off of the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded.

Outcome

1

2

3

4

5

6

Observed Frequency

62

45

63

32

47

51

Assuming the null hypothesis is that the observed frequency distributions are the same and the sample ² = 13.44, then at the 1% level of significance do we accept or reject the null hypothesis?

Select one:

A. Reject null hypothesis

B. Do Not Reject null hypothesis

C. Not enough information

D. None of the above

Degrees of freedom for chi square = 6-1=5

At 1% level table value =15.086

Calculated chi square=13.44 < 15.086, the table value

The null hypothesis is not rejected.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

62

50.

12.000

2.880

45

50.

-5.000

0.500

63

50.

13.000

3.380

32

50.

-18.000

6.480

47

50.

-3.000

0.180

51

50.

1.000

0.020

300

300

13.440

Outcome	1	2	3	4	5	6
Observed Frequency	62	45	63	32	47	51