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 p -value?
a. 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.
b. 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.
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 least 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 of at most 0.15 is 0.34.
e. 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:

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 least 0.15 is 0.34.

Step-by-step explanation:

The direction of the test is to the right of 0.15, because the researchers hypothesize that the proportion in region B is greater than the proportion in region A. The p-value is the probability of observing a sample difference of at least 0.15 if the null hypothesis is true.

You can use the fact that the p-value denotes the probability of the area to the right of the test statistic and symmetrically to the left(if the test is two tailed, else its just on the right tail)

The option that is the correct interpretation of the p-value is:

Option 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 least 0.15 is 0.34

A p value helps us to decide whether to accept or reject the null hypothesis. If the obtained p value is smaller than the level of significance, then we reject the null hypothesis else we accept it.

The p value shows the area to the right of the test statistic(in the right tail after the plot of test statistic on the x axis)

It shows both right and left tail symmetrically if the test is two tailed.

Since the test statistic is difference between the sample proportions and the alternate hypothesis is testing if the difference is greater than 0.15 or not. Thus, it is single tailed test.

Due to this, the p value is showing if the test statistic is 0.15 or to the right which is higher that 0.15 thus, p value is showing the probability that the test statistic is at least 0.15 is given by 0.34

Thus,

Option 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 least 0.15 is 0.34.

Learn more about p value here:

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