A few months before a statewide election, 584 individuals responded to a poll of

Question

A few months before a statewide election, 584 individuals responded to a poll of 1,000 randomly selected registered voters, indicating they favor candidate X for governor (p 1 = 0.5840). One month before the election, a second poll of 950 registered voters is conducted and 401 individuals respond who indicate they favor candidate X (p 2 = 0.4221). A 95% two-proportion z confidence interval for the true difference between the proportions favoring candidate X in the first and second polls was constructed and found to be (0.1181, 0.2057). Which of the following is the best interpretation of this interval? (4 points)

There has not been a significant decrease in support for candidate X.

There has been a significant decrease in support for candidate X.

There has been no change in support for candidate X.

Because the confidence interval is positive, candidate X is likely to win a majority of votes in the general election.

Because support for candidate X has decreased below 50%, this candidate is unlikely to win a majority of votes in the general election.

There has not been a significant decrease in support for candidate X.

There has been a significant decrease in support for candidate X.

There has been no change in support for candidate X.

Because the confidence interval is positive, candidate X is likely to win a majority of votes in the general election.

Because support for candidate X has decreased below 50%, this candidate is unlikely to win a majority of votes in the general election.

Explanation / Answer

I am not calculating the confidence interval myself and just answering on the basis of confidence interval given in the question.

Since a 95% confidence interval comes between 0.118 and 0.205, this means that there is a 95% probability that support has decreased and margin of decrease lies between these two numbers.

So, answer will. There has been a significant decrease in support for candidate X.

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