Question

Jorge was at the park playing with friends. He found a typical die with 6 sides on the ground. He took it home and rolled it 100 times and recorded the results (found in the table below). He wanted to see if the die was a 'fair die' or if it was weighted on one side so somone could cheat when playing games!

Is this a 'fair die' or has it been tampered with? Test at the α=0.10α=0.10 level of significance.

Which would be correct hypotheses for this test?

• H0:H0:The die is a fair die; H1:H1:The die has been tampered with
• H0:μ1=μ2H0:μ1=μ2; H1:μ1≠μ2H1:μ1≠μ2
• H0:p1=p2H0:p1=p2; H1:p1≠p2H1:p1≠p2
• H0:H0:The die has been tampered with; H1:H1:The die is a fair die

Roll count:

Rolled	Count
1	1
2	2
3	5
4	5
5	9
6	78

Test Statistic:



Give the P-value:



Which is the correct result:

• Reject the Null Hypothesis
• Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

• There is not enough evidence to suggest that the die has been tampered with.
• There is enough evidence to suggest that the die has been tampered with.

Answer 1

The statistical software output for this problem is:

Chi-Square goodness-of-fit results: Observed: Oi Expected: All cells in equal proportion N DF Chi-Square P-value 100 5 273.2 <0.0001

Hence,

Hypotheses: H0: The die is a fair die; H1: The die has been tampered with

Test statistic = 273.2

p - Value = 0.0000

Reject the Null Hypothesis

There is enough evidence to suggest that the die has been tampered with.