For this assignment, you will practice applying inferential statistical analysis to four business decision scenarios. Complete all of the given scenarios: Complete all of your scenario answers in one Word file and copy the Excel output, including graphics, into that document.
The average balance for customer accounts in The Reserve Fund at the time it was frozen by the Securities Exchange Commission (SEC) was $22,500, with a standard deviation of $7,500. The SEC overseers want to draw a sample of 100 accounts to help assess the impact of the fund's freeze on the account holders. Precisely (that is, by using specific numbers) what does the central limit theorem tell us regarding the sampling distribution of sample means for samples of this size from this population?
To complete this scenario, use the Sample Size Estimator Sheets A, B of this file.
In the early years of the twenty-first century, annual salaries for federal employees in the Upper Midwest averaged around $42,000, with a population standard deviation (σ) of $4,900. If we drew a random sample of 25 federal employees from this population:
- What would the standard error of the mean be?
- What is the probability that the sample mean would be between $41,000 and $43,000?
- What is the probability that the sample mean would be between $41,000 and $43,000 if we increased the sample size to 100?
To complete this scenario, use the Confidence Interval Calculator Sheets 1,2,3 and the Area Gas Prices – Random Sample Excel file, linked in the Resources.
The Minneapolis Star Tribune newspaper has decided to prepare an article regarding gasoline prices in the Twin Cities area (Minneapolis and St. Paul). The paper has designed a survey and taken a simple random sample of regular, unleaded gas prices at 35 area stations. The results are in the Area Gas Prices – Random Sample Excel file. Use this data to develop a 95 percent confidence interval for the average price of regular, unleaded gasoline in the area.
To complete this scenario, use the Confidence Interval Calculator Sheets 1,2,3.
The Sacred Grounds coffee shop in Deadhorse, AK, is considering replacing its coffee brewing units with new German brewers. You have been assigned to investigate this proposal. Make a 99% confidence interval for the average yield (cups per pound) for the new German coffee brewer. The margin of error should be no bigger than .3 (three-tenths of a cup). Based on the experience with the current system, your best guess for the population standard deviation is 1.2 cups. How big a sample do you require?