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 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. Assuming a significance level of 0.05, we can use a two-tailed z-test.

The null hypothesis (H0) is that there is no significant difference between the proportion of those favoring and not favoring casino gambling in the community. The alternative hypothesis (Ha) is that there is a significant difference.

We can calculate the test statistic using the formula:

z = (phat1 - phat2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where phat1 is the proportion favoring gambling (55/80), phat2 is the proportion not favoring gambling (25/80), p is the combined proportion (80/160), n1 is the sample size of those favoring gambling (80), and n2 is the sample size of those not favoring gambling (80).

Plugging in the values, we get:

z = (0.6875 - 0.3125) / sqrt(0.5*0.5*(1/80 + 1/80))
z = 3.24

This means that the difference in proportions is 3.24 standard deviations away from the expected proportion of no difference (based on the null hypothesis). This is a large enough difference to reject the null hypothesis and conclude that there is a significant difference between the proportions of those favoring and not favoring casino gambling in the community.

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