Consider testing the alternative hypothesis that the proportion of adult Canadians opposed to same-sex marriage in Canada is less than 0.5. The test was conducted based on a poll of n = 1003 adults and it had a p-value of 0.102. Which of the following describes the probability represented by the p-value for this test?
A) It is the probability that fewer than half of all adults in Canada that year were opposed to same-sex marriage.
B) It is the probability that more than half of all adult Canadians that year were opposed to same-sex marriage.
C) It is the probability that a sample of 1003 adults in Canada that year would result in 48% or fewer saying they are opposed to same-sex marriage, given that a majority (over 50%) of Canadian adults actually were opposed that year.
D) It is the probability that a sample of 1003 adults in Canada that year would result in 48% or fewer saying they are opposed to same-sex marriage, given that 50% of Canadian adults actually were opposed that year.

Question

Quizplus · Accepted Answer

The p-value represents the probability of observing a sample statistic as extreme as the one observed, or more extreme, under the assumption that the null hypothesis is true. In this context, the null hypothesis would be that the proportion of adult Canadians opposed to same-sex marriage is 0.5 (50%). Therefore, the p-value indicates the probability of obtaining a sample where 48% or fewer adults are opposed, assuming the true proportion opposed is 50%.

Consider Testing the Alternative Hypothesis That the Proportion of Adult