Question

The manager of a local fast-food restaurant is interested in improving the service provided to customers who use the restaurant's drive-up window. As a first step in this process, the manager asks his assistant to record the time it takes to serve a large number of customers at the final window in the facility's drive-up system. The results are in the file P07_08.xlsx, which consists of nearly 1200 service times. For this problem, you can assume that the population is the data in this file. Use Excel to generate a simple random sample of size 30 from the data. Round your answers to two decimal places, if necessary. a. Calculate a point estimate of the population mean from the sample selected above. What is the sampling error, that is, by how much does the sample mean differ from the population mean? b. Calculate a good approximation for the standard error of the mean. c. If you wanted to halve the standard error from part c, what approximate sample size would you need?

Answer 1

A point estimate is calculated from the sample mean. The standard error is approximated by dividing the sample standard deviation by the square root of the sample size. To halve this error, the sample size needs to be quadrupled.

Step-by-step explanation:

In the context of the scenario provided, where a manager wants to improve the service at a fast-food restaurant's drive-up window, we will address different aspects related to sampling and statistics:

1. Point Estimate: The point estimate of the population mean is the sample mean. It is computed by taking the sum of all observations in the sample and dividing by the sample size (n = 30). The sampling error is the difference between the sample mean and the population mean.
2. Standard Error: The standard error of the mean (SE) is a measure of the amount of variability in the sampling distribution of the mean. It can be approximated by dividing the sample standard deviation by the square root of the sample size.
3. To halve the standard error, you would need to increase the sample size to approximately four times the original sample size, since the standard error is inversely proportional to the square root of the sample size.