Question

When playing a board game, you notice that you seem to be rolling a lot of 6’s. Suspecting that the die may be loaded (in a way that favors rolling a 6), you give the die 50 test rolls. The die came up “6” a total of 15 times.

1. (4 pts) State a null hypothesis and alternative hypothesis (symbolically) to test the claim that the die is loaded (as you suspect it is).

2. (3 pts) List and check the appropriate assumptions/requirements for running the relevant hypothesis test.

3. (2 pts) Calculate the appropriate test value.

4. (4 pts) Calculate the p-value for this test, and explain what this number represents (your explanation should focus on what the p-value represents, not how we use the p-value to make a decision about rejecting the null hypothesis).

5. (4 pts) Using a significance level of α = .01, make the decision (reject or fail to reject H₀) and draw the appropriate conclusion regarding the original claim.

Answer 1

(a)

H0: Null Hypothesis: p = 1/6 = 0.1667 (The die is not loaded)

HA: Alternative Hypothesis: p 1/6 = 0.1667 (The die is loaded) (Claim)

(b)

The appropriate assumptions/requirements for running the relevant hypothesis test. are checked as follows:

(i) The dataare Simple Random Sample fromthe population of interest.

(ii) The population isat least 10 times as large as the sample

(iii) np = 50 X 1/6 = 8.3333 is not greater than or equal to 10. So, this condition is not satisfied.

(c)

n = 50

= 15/50 =0.30

Test Statistic is given by:

(d)

By Technology, p - value = 0.0114

Interpretation:

Given the null hypothesis: The die is not loaded is true, the p - value = 0.0114 is the probability of getting a result as or more extreme than the sample result by random chance alone.

(e)

Since p - value= 0.0114 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the die is loaded.