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

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.

1. The numerical value of A is:
   Enter answer as an integer or a decimal rounded to 3 places if appropriate.
2. The Null Hypothesis is:   
3. (A) The Null 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.)
4. (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.)

5. Enter answer by selecting the appropriate letter.

Answer 1

The die is rolled 24 times. So expected frequency = 24*(1/6)=4

So all the expected frequencies will be 4

Hence value of A=4

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.)

Statistical test will be chi sq test. And the test statistic is =

Summation (Expected freq-observed freq) ^2/Expected freq

so the chi sq test statistic is 14.5 and critical value of chisq with degrees of freedom 5 is 5.333

Conclusion : As observed value 14.5 > critical value 5.33 we reject the null hypothesis at 5% level and conclude that the die is biased.