Question

select the correct answer. a clothing retailer is gathering data on the amount of time each customer spends shopping in its stores. each location collected 20 pieces of data and will compile that data to determine a population mean. one location has a sample mean of 32.5. which statement must be true about this situation? a. the population mean must be less than 32.5. b. the population mean must be greater than 32.5. c. the population mean is also 32.5. d. there is not enough information to make a conclusion about the population mean.

Explanation:

Step1: Understand sample - population relationship

A sample mean is an estimate of the population mean. Just because one sample (from one location with a sample size of 20) has a mean of 32.5, we cannot make definitive statements about the population mean.

Step2: Analyze each option

• Option A: We cannot say the population mean must be less than 32.5 just based on one sample.
• Option B: We cannot say the population mean must be greater than 32.5 just based on one sample.
• Option C: We cannot assume the population mean is exactly 32.5 just because a sample has that mean.
• Option D: Since we only have one sample from one location, there is not enough information to make a conclusion about the population mean.

Answer:

D. There is not enough information to make a conclusion about the population mean.