Final answer:
The point estimate of the proportion of items returned at the Houston store is 15%. The 95% confidence interval for the proportion of returns at the store ranges from 7.2% to 22.8%.
Step-by-step explanation:
According to the University of Nevada Center for Logistics Management, a Houston department store found that 12 out of 80 items sold in January were returned. To address the student's question:
a. Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.
The point estimate for the proportion of items returned is simply the number of items returned divided by the total number of items sold. Therefore, the point estimate is 12/80 = 0.15 or 15%.
b. Construct a 95% confidence interval for the proportion of returns at the Houston store.
To construct the 95% confidence interval, we use the formula for the confidence interval of a proportion: point estimate ± (z * sqrt((point estimate * (1 - point estimate)) / n)), where z is the z-score corresponding to the 95% confidence level (approximately 1.96), and n is the sample size (here 80).
Substituting the values:
0.15 ± (1.96 * sqrt((0.15 * (1 - 0.15)) / 80))
= 0.15 ± (1.96 * sqrt((0.15 * 0.85) / 80))
= 0.15 ± (1.96 * sqrt(0.1275 / 80))
= 0.15 ± (1.96 * 0.0398)
= 0.15 ± 0.078
= (0.072, 0.228)
The 95% confidence interval for the proportion of returned items at the Houston store is between 7.2% and 22.8%.