Question

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. Perform a hypothesis test at 5% level of significance. Show all the steps for a hypothesis test at 5% level of significance

Answer 1

As we are trying to test here whether the dropout rate has decreased, therefore the null and the alternative hypothesis here are given as:

Now as this is a one tailed test, the test statistic here is computed as:

Now as this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z < -1.8544) = 0.0318

As the p-value here is 0.0318 < 0.05, therefore the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that the dropout rate has decreased.