In "An Informal Look at Use of Bakery Department Tongs and Tissues," a researcher named Trinkaus reported: "Of 108 people observed extracting for purchase rolls or pastries from displayed bulk stock in food supermarket bakery departments, about 90% used their hands for item selection and withdrawal rather than the store provided tongs. In stores where tissues were provided instead of tongs, approximately 60% of the 133 people who were observed used their hands."

a. The overall proportion using their hands was . Explain why this is not the exact average of 0.90 and 0.60 (which is 0.75).

b. The P-value for the test of a relationship between use of hands and having tissues or tongs provided is 0.000. Is the chisquare statistic much less than 3.84, a bit less than 3.84, a bit more than 3.84, or much more than 3.84?

c. Explain how the study's results may be biased if observations were made in the morning for stores with tongs and in the evening for stores with tissues.

d. Explain how the study's results may be biased if stores with tongs tended to be located in areas with a large student population.