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Chapter 8: Problem 66

You are working for a supermarket. The manager has asked you to estimate the mean time taken by a cashier to serve customers at this supermarket. Briefly explain how you will conduct this study. Collect data on the time taken by any supermarket cashier to serve 40 customers. Then estimate the population mean. Choose your own confidence level.

Short Answer

Expert verified
To conduct the study, collect the service time for 40 customers, calculate the sample mean, and then estimate the population mean using the chosen confidence level. Report these findings in a formal document.

Step by step solution

01

Data collection

Start by observing and timing how long a cashier takes to serve each of the 40 customers. This can be done using a stopwatch or a timing device and record these times accurately.
02

Calculate the Sample Mean

Once the times are collected, calculate the sample mean. This is done by adding up all the 40 recorded times and dividing by 40, the number of customers.
03

Estimate the Population Mean

In order to estimate the population mean, we can use the sample mean. The confidence level will determine the accuracy of our estimation. For example, a 95% confidence level means we are 95% sure that the population mean lies within a certain range of the sample mean. Apply the appropriate statistical formula to determine this range. Make sure to note that this will be an estimation and not the actual population mean. For this, the exact formula will depend on the statistical test you choose (like z-test or t-test) and would also require either the population standard deviation (for z-test) or sample standard deviation (for t-test).
04

Report the Results

Once the population mean is estimated using the chosen confidence level, prepare a report with the findings. This should include the methodology used, the sample mean, the estimated population mean and the confidence level.

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Most popular questions from this chapter

You are interested in estimating the mean age of cars owned by all people in the United States. Briefly explain the procedure you will follow to conduct this study. Collect the required data on a sample of 30 or more cars and then estimate the population mean at a \(95 \%\) confidence level. Assume that the population standard deviation is \(2.4\) years,

a. How large a sample should be selected so that the margin of error of estimate for a \(98 \%\) confidence interval for \(p\) is \(.045\) when the value of the sample proportion obtained from a preliminary sample is \(.53\) ? b. Find the most conservative sample size that will produce the margin of error for a \(98 \%\) confidence interval for \(p\) equal to \(.045\).

For each of the following, find the area in the appropriate tail of the \(t\) distribution. a. \(t=2.467\) and \(d f=28\) b. \(t=-1.672\) and \(d f=58\) c. \(t=-2.670\) and \(n=55\) d. \(t=2.383\) and \(n=23\)

A gas station attendant would like to estimate \(p\), the proportion of all households that own more than two vehicles. To obtain an estimate, the attendant decides to ask the next 200 gasoline customers how many vehicles their households own. To obtain an estimate of \(p\), the attendant counts the number of customers who say there are more than two vehicles in their households and then divides this number by 200. How would you critique this estimation procedure? Is there anything wrong with this procedure that would result in sampling and/or nonsampling errors? If so, can you suggest a procedure that would reduce this error?

a. How large a sample should be selected so that the margin of error of estimate for a \(99 \%\) confidence interval for \(p\) is \(.035\) when the value of the sample proportion obtained from a preliminary sample is \(.29\) ? b. Find the most conservative sample size that will produce the margin of error for a \(99 \%\) confidence interval for \(p\) equal to \(.035\).
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