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. At a 5% significance level, the decision is to ________. A) reject H₀; we can conclude that the high school dropout rate has decreased B) reject H₀; we cannot conclude that the high school dropout rate has decreased C) do not reject H₀; we can conclude that the high school dropout rate has decreased D) do not reject H₀; we cannot conclude that the high school dropout rate has decreased

Question

Quizplus · Accepted Answer

The polling company's survey found a lower dropout rate than the Institute of Education Sciences' rate, so the polling company would like to determine whether the dropout rate has decreased. The null hypothesis (H0) is that the dropout rate has not decreased, and the alternative hypothesis (Ha) is that the dropout rate has decreased. The polling company would like to test the null hypothesis at a 5% significance level. The p-value for the test is the probability of getting a sample dropout rate as low as or lower than 6.5% if the null hypothesis is true. The p-value is less than 0.05, so the polling company would reject the null hypothesis and conclude that the high school dropout rate has decreased.

The Institute of Education Sciences Measures the High School Dropout