A product manager is concerned that one of her product’s brand share may be unevenly distributed throughout her firm’s product market

1) A product manager is concerned that one of her product’s brand share may be unevenly distributed throughout her firm’s product market. In a survey in which the firm’s product market was divided into four geographic regions, a random sampling of 100 customers in each region was surveyed, with the following results:

Develop a table of observed and expected frequencies for the above.

2) For problem 1):

a)      Calculate the sample c² value.

b)      State the null and alternative hypothesis.

c)      At a = .05, test whether the brand share is the same across the four regions.

3) The following pairs of observations were collected:

a)      Plot the values of X and Y. What relationship does the scatter diagram suggest?

b)      Find the least squares line.

c)      Find the predicted value for each value of X.

d)     Find the residual for each predicted value of Y.

e)      Verify that the sum of the residuals in part d) is zero.

4) The following data show the number of annual bankruptcies (X) in hundreds at a bankruptcy court and the number of personnel who had to process the bankruptcies (Y).

a)      Estimate the standard deviation of the error for the regression model.

b)      Show that the mean of the residuals for the bankruptcy data is zero.