Question

In 1947​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1100 adults​ surveyed, 363 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 319 indicated that they were total abstainers. Use the α =0.01 level of significance.

1) Find the test statistic for this hypothesis test.

2) Determine the​ P-value for this hypothesis test.

Answer 1

From the given information:

p1 = 363/1100 = 0.33

p2 = 319/1100 = 0.29

n1 = n2 = 1100

We need to test the difference in proportions. We will use a two-sample z-test for proportions.

Ho: p1 - p2 = 0

Ha: p1 - p2 =/ 0

The formula for the test statistic is:

p-bar = (363 + 319)/(1100 + 1100) = 0.31

Inputting the values in the formula, we get:

z = 2.029

b) The p-value for the test = .04236

As the p-value < 0.05, we can reject the null hypothesis. We conclude that there is a significant difference in the proportions.