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

Answer:

Mean: 0.400

Standard error: 0.022

Step-by-step 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:

$\sigma_p=\sqrt\dfrac{p(1-p)}{N}}=\sqrt\dfrac{0.4*0.6}{500}}=\sqrt{0.00048}=0.022$

being p: population proportion, N: sample size.