Fifty-five voters from a sample of 80 indicated that they favored casino gambling in their city. The city council is interested in finding out whether or not there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. The test statistic is ______.
A) 0.50
B) 3.71
C) 80
D) 3.24

Question

Quizplus · Accepted Answer

To determine the test statistic, we need to conduct a hypothesis test for the difference in proportions.

Let p be the proportion favoring casino gambling in the population.

Null Hypothesis: p = 0.5 (Assuming equal proportion of people favoring and not favoring casino gambling)
Alternative Hypothesis: p ≠ 0.5 (There is a significant difference between the proportions of those favoring and not favoring casino gambling)

Using the formula for the test statistic for difference in proportions:

z = (phat - p0) / sqrt(p0(1-p0)/n)

where phat is the sample proportion, p0 is the null hypothesis proportion, and n is the sample size.

plugging in the values, we get:

z = (55/80 - 0.5) / sqrt(0.5*0.5/80)
z = 3.24

Therefore, the test statistic is 3.24.

Thus, the correct answer is D.

Fifty-Five Voters from a Sample of 80 Indicated That They