Question

Tutoring Services: Suppose that 40% of community college students never use tutoring services available at their college. Suppose we randomly select samples of community college students. 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

Answer 1

Answer: The mean and standard error of the sampling distribution of sample proportions are 0.40 and 0.0219 respectively.

Explanation:

Formula : Mean of the sampling distribution of sample proportions

`\mu_p= p`

Standard error of the sampling distribution of sample proportions

`\sigma_p=\sqrt{(p(1-p))/(n)}`

, where p = population proportion

n= sample size

Here, p =0040

n= 500

So , Mean of the sampling distribution of sample proportions

`\mu_p= 0.40`

Standard error of the sampling distribution of sample proportions

`\sigma_p=\sqrt{(0.40(1-0.40))/(500)}\\\\=\sqrt{\sdfrac{0.40*0.60}{500}}\\\\=\sqrt{(0.24)/(500)}\\\\=√(0.00048)\\\\\approx0.0219`

Hence, mean and standard error of the sampling distribution of sample proportions are 0.40 and 0.0219 respectively.