Problem One

Suppose that an automotive parts and accessories chain is experimenting with a new sales promotion. Two similar stores are selected for the experiment. For Store 1, nothing changes. This store constitutes the control group. For Store 2, the treatment group, the promotion is implemented.

Sales in hundreds of dollars over a five-day period are as follows:
Control: 6, 6, 7, 10, 12, 9, 6, 5, 5, 7
Treatment: 2, 5, 2, 4, 7, 1, 2, 3, 4, 5
The expectation that sales will be higher in the treatment group makes this a one-tailed test; the alternate hypothesis is m1 < m2. Use Excel to determine whether differences between the two groups are statistically significant.
Show all of your work and clearly label each of your calculations. Share your calculations and your interpretations of your findings in your Word document.

Problem Two

Suppose that a home builder is approached by a customer who wants to move in as soon as possible. The customer chooses three home designs that she likes and asks the home builder which one could be completed the fastest. To compare the three designs on speed of completion, the builder randomly selects 10 homes that he built in the past based on each of the three designs.
Use the Excel Analysis ToolPak to run an ANOVA test in order to determine which design would be best for the customer. Show all of your work and clearly label each of your calculations. Make sure to also clearly describe the respective data and your conclusions.

The data for the number of days to build each home are as follows:
Design A: 15, 17, 19, 21, 23, 25, 27, 29, 31, 33
Design B: 29, 34, 39, 44, 49, 54, 59, 64, 69, 74
Design C: 22, 24, 25, 27, 28, 28, 29, 31, 33, 34
For more information on conducting an ANOVA test in Excel reference the Week Two Recommended Resources.

Problem Three

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. Now there are concerns that if the true mean is actually higher than this they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set significance , test to see if the insurance company should be concerned.