Question

1. An experiment was done to determine if a pair of dice is “fair”, that is, the probability that each number on each die is the same. Tom tosses the dice 50 times and determines that the mean sum of the sample is 6.6, with a standard deviation of 1. 133. According to the mechanics of tossing two dice, the mean should be 7. Determine if this is a fair dice at the .05 level of significance. Also determine the p-value.

1. Determine if a t or a z hypothesis test should be used.
2. Is this a one-tail or a two-tail hypothesis test?
3. Find H0 and H1.
4. Use both the Classical Approach and the P-Value Approach to determine whether to reject or fail to reject the null hypothesis.
5. Interpret the conclusion.

Answer 1

Null Hypothesis H0: The dice is fair. = 7

Alternative Hypothesis Ha: The dice is not fair. 7

This is two-tail hypothesis test.

Sample mean, = 6.6

Sample standard deviation s = 1.133

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s /  = 1.133 /  = 0.1602304

Test statistic, t = ( - ) / SE =  (6.6 - 7) / 0.1602304 = -2.496

Degree of freedom = n-1 = 50-1 = 49

Critical value of t at .05 level of significance and df = 49 is  2.01

Classical Approach - Since the test statistic does not lie between -2.01 and 2.01, we reject null hypothesis H0.

For two-tail test, p-value = 2 * p(t < -2.496, df = 49) =  0.01597

P-Value Approach - Since, p-value is less than 0.05 significance level, we reject null hypothesis H0.

There is sufficient evidence at 5% significance level to conclude that the dice is not fair.