# Statistics Assignment | Professional Writing Services

1. 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)
2. Construct a 95% confidence interval for the mean account balance of the population.
3. What is the margin of error for estimating the mean account balance at the 95% confidence level.
4. 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.
5. 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?

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1. 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)
2. Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.
3. What is the margin of error at the 95% confidence level?
4. 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?
1. 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)
2. 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?
3. How large should the sample size be if the desired margin of error is 25 seconds?
1. 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)

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