What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
A).0075
B).03
C).075
D).3
E).75

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution for a sample proportion can be calculated using the formula:

standard deviation = √(p(1-p)/n)

where p is the true proportion, and n is the sample size. Since we don't know the true proportion of failures in this scenario, we can use the sample proportion as an estimate. Assuming a sample size of at least 30, the sample proportion can be treated as approximately normally distributed, and we can use a standard deviation estimate of:

√(p(1-p)/n) ≈ √(0.25/n) = 0.5/√n

For a sample size of n=100, this gives us a standard deviation estimate of approximately 0.05 or 0.06. Since none of the answer choices are exactly equal to this estimate, the closest choice is B (0.03).

What Is the Estimate of the Standard Deviation of the Sampling