Question

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 101. What is the probability that the sample proportion will be within 3 percent of the population proportion?

Answer 1

0.5137

Explanation:

The margin of error equals the critical value times the standard error.

MoE = CV × SE

In this case, the critical value is the z-score.

For a proportion, the standard error is:

SE = √(pq/n)

SE = √(0.75 × 0.25 / 101)

SE = 0.04309

Therefore:

0.03 = z × 0.04309

z = 0.6963

So the probability is:

P(-0.6963 < Z < 0.6963)

= P(Z < 0.6963) − P(Z < -0.6963)

= 0.7569 − 0.2431

= 0.5137