Suppose that you were trying to determine if the population

Suppose that you were trying to determine if the population proportion of Americans, that believe that public day care is very suitable for children under the age of 3, is less than 25%. You decide to test the null hypothesis Ho: p = 0.25 versus Ha: p < 0.25.

In 1988, the General Social Survey included a question that asked its participants if they think that government day care for children under the age of 3 was very suitable. Out of the 1262 surveyed, 259 said yes. What is the value of the test statistic for this problem?

Solution

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(259/1262-0.25)/sqrt(0.25*0.75/1262)

=-3.67

Answer: -3.67