# Kruskal- Wallis test , scatter plot, regression equation

18.6 A business that is interested in starting an on-line shopping service is interested in finding out whether or not there are differences in how women shop on-line. They are interested in capturing people who are already connected to the Internet, so they run a Web. based survey. They ask respondents how many purchases they have made on-line in the last three months. In addition, they ask demographic questions about gender, age, and level of education. The data for women respondents in three age categories are shown below:

21-30 30-45 45-60

2 4 3

2 5 3

3 6 4

4 6 5

4 8 6

5 9 6

8 9 9

(b) Set up the hypotheses to see if there is a difference in the number of purchases made on-line by women for the three age groups.

(c) Find the rank for each data value, and find the rank sum and average rank for each sample.

(d) Perform the Kruskal- Wallis test at the 0.05 level of significance. What can you conclude?

15.25 The British Bankers' Association wanted to look at the relationship between the amount of deposits made (in billions of Â£) and the number of customers that a bank had. Analysts collected data on six different large banks and found the following information:

Bank Name Deposits (Â£ billion) Customers (million)

Abbey National 101.7 13.6

Barclays 108.2 10.0

Lloyds 96.9 15.0

National Westminster 113.8 7.5

Woolrich 27.5 4.0

Halifax 77.1 7.6

(a) Which variable is the independent variable? Which is the dependent variable?

(b) Create a scatter plot of the data. Does it appear that the amount of deposits is related to the number of customers?

(c) Find the equation of the regression line for the data-

(d) Plot the regression line on the same plot as the data. Do you think that the line does a good job of predicting the amount of deposits? Why or why not?

(e) Calculate the standard error of the estimate, Sylx' for the regression line.

(f) At the 0.05 level, is the model significant?

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