Question

Market researchers selected a random sample of people from region A and a random sample of people from region B. The researchers asked the people in the samples whether they had tried a new product. The difference between the sample proportions (B minus A) of people in the regions who indicated they had tried the new product was 0.15. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportion of B is greater than that of A. The p-value of the test was 0.34.Which of the following is the correct interpretation of the pp-value?If the difference in proportions of people who have tried the new product between the two populations is actually 0.15, the probability of observing that difference is 0.34.A. If the difference in proportions of people who have tried the new product between the two populations is actually 0.34, the probability of observing that difference is 0.15.B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.C. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at most 0.15 is 0.34.D. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference equal to 0.15 is 0.34.

Answer 1

B. If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34.

Explanation:

Null hypothesis:

H0: The population proportion B = population proportion A

Alternative hypothesis:

H1: The population proportion of B > population proportion A

The P value, also called calculated probability, is that of getting test results which are at least as extreme as the results which were observed in a Statistical test. We assume the null hypothesis to be true.

Therefore if the population proportion of B = A (H0 is true), then we conclude that the probability of observing a difference of at least 0.15 is = 0.34.