11 May Consider the Sum of Two Dice scenario below
Consider the Sum of Two Dice scenario below. Perform the required experiment and hypothesis test by completing the eight steps.
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Sum of Two Dice
Are your dice loaded? When playing with honest, or balanced, dice, the random variable X representing the sum of the numbers on the faces when two dice are rolled possesses the following probability distribution:
| x | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| p(x) | 0.028 | 0.056 | 0.083 | 0.111 | 0.139 | 0.167 | 0.139 | 0.111 | 0.083 | 0.056 | 0.028 |
Furthermore, the mean of the distribution, μ = 7 and the standard deviation, σ = 2.4152.
Examine the average sum of two dice rolled 40 times. Do your dice appear to be fair? Perform a test of the null hypothesis that the mean sum is 7.
Steps for your analysis:
1. Roll two dice 40 times. Record the sum of numbers on the faces of the two dice each time. Find the mean sum for your sample.
2. Indicate the null and alternative hypotheses.
3. Indicate the distribution that the sampling distribution of your sample mean follows and justify your reasoning. In other words, will your test statistic follow a z distribution, a t distribution, or some other distribution, and how do you know?
4. Calculate your test statistic.
5. State the rejection region.
6. Compare the test statistic against the critical value for the rejection region, and state your conclusion.
7. Interpret your conclusion within the context of the experiment.
8. Determine the observed significance level (p-value) of your test.
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