Question

Tutoring Services: The Community College Survey of Student Engagement reports that 46% of the students surveyed rarely or never use peer or other tutoring resources. Suppose that in reality 40% of community college students never use tutoring services available at their college. In a simulation we select random samples from a population in which 40% do not use tutoring. For each sample we calculate the proportion who do not use tutoring. If we randomly sample 500 students at a time, what will be the mean and standard error of the sampling distribution of sample proportions? Mean: (Round to two decimal places.) Standard error: (Round to exactly three decimal places.)

Answer 1

Mean: 0.400

Standard error: 0.022

Explanation:

We are taking samples of size n=500 out of a population with parameter p=0.40.

The expected distribution is the sampling distribution of sampled proportions. This distribution has parameters that are calculated as:

Mean: the mean of the sampling distribution is equal to the population proportion, as it is not biased.

In this case, the mean of this sampling distribution is p=0.40.

Standard error: the standard error depends on the population proportion and the sample size. It is calculated as:

`\sigma_p=\sqrt(p(1-p))/(N)}=\sqrt(0.4*0.6)/(500)}=√(0.00048)=0.022`

being p: population proportion, N: sample size.