For each potential customer entering an auto showroom, the type of vehicle desired is recorded. Table 17.4.1 shows data for the past week, together with percentages for the past year at this time.

a. Find the percentages for last week’s vehicles.

b. Compare last week’s percentages to last year’s percentages. Describe any differences you see in terms that would be useful to an automobile salesperson.

c.* Assuming last year’s percentages continued to apply, how many of these 536 people would you expect to be looking for an economy car? Compare this to the observed number of such people.

d.* Find the expected count for each type of vehicle, assuming last year’s percentages still apply.

e.* Find the chi-squared statistic, viewing last year’s percentages as exact.

f. Discuss the assumptions required for the chisquared test to be valid. In particular, what population are you inferring about?

g. How many degrees of freedom are there for this chisquared test?

h. Find the appropriate chi-squared table value for the 5%, 1%, and 0.1% levels.

i. Perform the chi-squared test at each of these levels and report the results.

j. State your conclusions (with a p-value reported as p > 0.05, p < 0.05, p < 0.01, or p < 0.001), discussing any shifts in consumer preferences.

TABLE 17.4.1 Vehicle Desired Last Week's ype Family sedarn Economy car Sports car Count 187 206 29 Last Year's Percentages 25.8% 46.2 an 72 12.4 Pickup 42 7.5 Total 536 100.0%