Refer to the Information Provided in Scenario 36

question 73

Multiple Choice

Refer to the information provided in Scenario 36.3 below to answer the question(s) that follow.
SCENARIO 36.3: Consider a local high school that has 300 sophomores considered to be at-risk students. A privately-sponsored after-school sports program has been established to try to help at-risk students succeed in finishing high school. The local government wants to know if this program reduces the students' probability of dropping out of high school before the end of their junior year, and decides to randomly sample 150 of the 300 at-risk sophomores and invite them to attend the after-school program at no cost. 100 students accept the invitation, and by the end of their junior year, the drop-out percentage of the 100 students who attended the program was lower than the drop-out percentage of the 200 students who did not attend the program.
-Refer to Scenario 36.3. The efficacy of this program can be best measured by comparing

• A) the drop-out percentage of the 100 students who attended the program to the drop-out percentage of the 200 students who did not attend the program.
• B) the drop-out percentage of the 100 students who attended the program to the drop-out percentage of the 50 students who were offered the program but chose not to attend.
• C) the drop-out percentage of the 150 students who were offered the program to the drop-out percentage of the 150 students who were not offered the program.
• D) the drop-out percentage of the 50 students were offered the program but chose not to attend to the drop-out percentage of the 150 students who were not offered the program.

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Definitions:

Central Limit Theorem

A statistical principle stating that with a large enough sample size, the distribution of the sample means will be approximately normally distributed, regardless of the population's distribution.

Sample Size

The number of observations or data points selected from a population for statistical analysis.

Central Limit Theorem

A statistical theory that states the distribution of sample means approximates a normal distribution as the sample size becomes large, regardless of the population's distribution.

Sampling Distribution

The sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population.