Statistics 2501 (001)
Assignment #5: Nov. 7, 2003
Due in class: Nov. 17, 2003

All problem numbers are from the textbook Statistics for Business and Economics, 8th Edition.

1. In an analysis of a catalog store chain's operations, the general manager wants to see if the time (in minutes) it takes to unload its catalogues from a truck depends on the total weight of the boxes (in hundreds of pounds) and the time of day when the truck is unloaded (morning, early afternoon or late afternoon).

   You can access the data for use in Minitab by opening a worksheet, and looking for the file catalogue.MTW under Pub on `CS-thebe' and stat2501. In the file, the column TimeofDay contains 1 = morning, 2 = early afternoon, 3 = late afternoon.

   Now, answer the following:

   1. Use Minitab to create a plot, where unloading time is on the $y$ axis, weight is the $x$ axis, and you have different numbers on your plot to represent the time of day. See the example from class on sales, traffic flow and city to get an idea of what you want to construct.

      To do this in Minitab, you will want to use Annotation - labels when plotting, where the labels will be from your TimeofDay column.

      Describe the relationship between unloading time and weight. Does unloading time seem to also depend on the time of day?

   2. Write a regression model relating unloading time ($y$) to weight ($x_{1}$) that allows for different slopes for the different times of day.

   3. Fit the model of (b) and report your least squares regression line.

   4. Are the slopes associated with the three possible times of day different? Test at $\alpha = 0.01$.

2. A well-executed completely randomized experiment was conducted by the star students of Stats 2501. Data was collected on the number of chocolate chips or chunks contained within 3 brands of cookies.

   You can access the data for use in Minitab by opening a worksheet, and looking for the file cookies.MTW under Pub on `CS-thebe' and stat2501. In the dataset, CAhoy is Chips Ahoy, OurComp is Our Compliments and Purity is Purity brand.

   1. Use Minitab to construct boxplots for the number of chocolate chips (chunks) in each brand of cookie. Make sure the plots appear side-by-side on the same graph. Does it appear that the mean number in each brand differ?

   2. Does it appear that all 3 cookies contain the same average number of chocolate chips? Test at $\alpha = 0.05$.

   3. Based on your answer to (b), does it make sense to move on to construct confidence intervals to compare the treatment means? Explain why or why not.

   4. Regardless of your answer in (c), use the Bonferroni method to construct 90% confidence intervals for the difference between the mean number of chocolate chips (chunks) in (i) Chips Ahoy and Our Compliments (ii) Our Compliments and Purity. Interpret these intervals.

      To get the exact t-value you need, you can follow this Minitab example. If you needed $t_{0.1}$ using 11 df:

      First, select Calc - Probability Distributions - t

      Then, choose Inverse Cumulative Probability, supply 11 for df, and 0.9 for Input constant. (Why 0.9?). When you're ready, click OK.

      On the screen, this gives you an answer for $t_{0.1}$. Of course, you will replace 0.9 by the appropriate value you need, and the degrees of freedom by those you find in this problem.

3. Refer to the data in #14.46, p. 863, and complete the following. The data can be accessed for use in Minitab by opening a worksheet, and looking for the file supermkt.MTW under Pub on `CS-thebe' and stat2501.
   1. Identify the (i) response variable; (ii) factors; (iii) number of levels of each factor and (iv) number of treatments in this problem.

   2. Test at $\alpha = 0.1$ if display and price interact in affecting the sales.

   3. Based on your answer above, is it appropriate to conduct main effects tests? Explain why or why not.

4. Refer to the data in #15.8, p. 893-894. Does it appear that the median age of the terminated employees exceeds the entire company's median age? Clearly state the appropriate hypothesis and test statistic, and base your conclusion on your p-value. Do this problem by hand (not using Minitab).