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QUESTION
A simple random sample of 80 customers is selected from an account receivable portfolio and the sample mean account balance is $1250. The population...
- A simple random sample of 80 customers is selected from an account receivable portfolio and the sample mean account balance is $1250. The population standard deviation σ is known to be $250. (8 points)
- Construct a 95% confidence interval for the mean account balance of the population.
- What is the margin of error for estimating the mean account balance at the 95% confidence level.
- Construct a 95% confidence interval for the mean account balance of the population if the sample mean account balance is obtained from a random sample of 150 instead of 80.
- Based on the results from a. and c., what can you say about the effect of a larger sample size on the length of the confidence interval at the same confidence level?
- A simple random sample of 50 calls is monitored at an in-bound call center and the average length of the calls is 6.5 minutes. The population standard deviation σ is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4.5 minutes. (6 points)
- Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.
- What is the margin of error at the 95% confidence level?
- Do we need to make any assumption on the distribution of the length of in-bound calls at this call center? Why or why not?
- According to a previous study, check out times at a supermarket are between 3 to 6 minutes (180 to 720 seconds.) A survey involving a random sample of customers of the supermarket is planned and the first order of business is to decide on an appropriate sample size. The 95% level of confidence will be used. (4 points)
- What is the planning value for the population standard deviation to be used in the sample size formula for estimating the population mean check-out time?
- How large should the sample size be if the desired margin of error is 25 seconds?
- In a survey, the planning value for the population proportion is p* = 0.28. How large should the sample size for the survey be if the desired level of confidence is 95% and the desired margin of error is 0.035? (2 points)
