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 100 students from this population, the standard error is approximately 5%. Would it be unusual to see 46% who do not use tutoring in a random sample of 100 students?

Answer 1

Answer:

No, this would not be unusual because 46% is only 1.2 standard errors from 40%

Step-by-step explanation:

Consider the provided information.

The standard error is approximately 5%

Standard error(SE)=0.05

As we know $SE=\frac{\sigma}{\sqrt{n} }$

Here x=46%=0.46 and μ=40%=0.40

Now use the formula: $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

Substitute the respective values in the above formula.

$z=\frac{0.46-0.4}{0.05}$

$z=1.2$

Hence, this would not be unusual because 46% is only 1.2 standard errors from 40%