Exhibit 9-6.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.In 2009,the high school dropout rate was 8.1%.A polling company recently took a survey of 1000 people between the ages of 16 and 24 and found 6.5% of them are high school dropouts.The polling company would like to determine whether the dropout rate has decreased. Refer to Exhibit 9-6.At a 5% significance level,the p-value and are _____________.

Question

Exhibit 9-6.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.In 2009,the high school dropout rate was 8.1%.A polling company recently took a survey of 1000 people between the ages of 16 and 24 and found 6.5% of them are high school dropouts.The polling company would like to determine whether the dropout rate has decreased. Refer to Exhibit 9-6.At a 5% significance level,the p-value and  are _____________.

Quizplus · Accepted Answer

To determine if the dropout rate has decreased, we need to conduct a hypothesis test. 
Null hypothesis: The dropout rate is still 8.1%. 
Alternative hypothesis: The dropout rate is less than 8.1%. 
Since the sample size is greater than 30, we can use a z-test. 
The z-value is calculated as: 
z = (sample proportion - null proportion) / standard error 
z = (0.065 - 0.081) / sqrt((0.081 * 0.919) / 1000) 
z = -2.62 
Using a z-table or calculator, we find that the p-value is approximately 0.004. 
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the dropout rate has decreased. 
The correct answer is B, with the p-value given in scientific notation.