In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. the students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168.

John is a 45-year-old manager who enjoys playing basketball in his spare time with his teenage sons and their friends. at work he finds that he is better able to solve problems that come up because of his many years of experience, but while on the court, he finds he is not as good keeping track of the ball while worrying about the other players. john's experience is:

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.

Which is cheaper: eating out or dining in? the mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04 (money.msn website, november 7, 2012). a sample of 100 neighborhood restaurants showed a mean price of $12.75 and a standard deviation of $2 for a comparable restaurant meal. a. develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home. b. using the sample from the 100 restaurants, what is the p-value? c. at a = .05, what is your conclusion? d. repeat the preceding hypothesis test using the critical value approach