Question 11 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A student believes that a certain 6-sided number cube, with the numbers 1 to 6, is unfair and is more likely to land with a 6 facing up. The student rolls the cube 100 times and lands with 6 facing up 20 times. The P-value for the test of the hypotheses, H0:p=0.17 and Ha:p>0.17, is 0.19. What is the correct conclusion given a=0.05?
Answer
A
Because the P-value is less than a=0.05, the student should reject H0.
B
Because the P-value is less than a=0.05, the student should fail to reject H0.
C
Because the P-value is greater than a=0.05, the student should reject H0.
D
Because the P-value is greater than a=0.05, the student should fail to reject H0.
Explanation
Compare the P-value, 0.19, with the significance level, 0.05. Since 0.19 is greater than 0.05, the result is not statistically significant, so there is not enough evidence to support the claim that the cube lands on 6 more often than 17% of the time. The student should fail to reject H₀, which is choice D.
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