Q. 20 - The Practice of Statistics for AP

Question

An online poll posed the following question: 

It is now possible for school students to log on to Internet sites and download homework. Everything from book reports to doctoral dissertations can be downloaded free or for a fee. Do you believe that giving a student who is caught plagiarizing an F for their assignment is the right punishment? 

Of the $20,125$ people who responded, $14,793$ clicked “Yes.” That’s $73.5\%$ of the sample. Based on this sample, a $95\%$ confidence interval for the percent of the population who would say “Yes” is $73.5\%$ $\pm 0.61$. Which of the three inference conditions is violated? Why is this confidence interval worthless? 

Step-by-Step Solution

Answer

The inference conditions violated are:

Random, Voluntary response sample.

Step 1: Given Information

Violated inference condition

Three inference conditions: Normal, Independent, Random

The condition of Random was violated, because the sample is collected by an online poll which results in a voluntary response sample and thus not a random sample.

Step 2: Explanation

We should point out that the sample of $20,125$ people is made up of people who elected to participate, making it a voluntary response sample.

Because persons with the strongest opinions are more likely to engage in voluntary response sampling, the population results are likely to diverge significantly from the sample results.

Because the percentage of $73.5$ percentage . is not a credible measurement for the population percentage, the confidence interval is unlikely to contain the true value of the population proportion.