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The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Let {Xn : n >=1} be a sequence of positive independent random variables with E(Xn) = c 2 (0; 1) for each n. Let Yn = X1X2...Xn, the product of the Xi's. Use Markov's inequality to prove that Yn ~ 0 in probability.
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In a survey of the 3000 boy scouts in the National Capital Area Council (NCAC), it is found that they have a mean weight of 135 lbs with a standard deviation of 15 lbs. How many of the boy scouts have weights between 120 lbs and 150 lbs.?
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a researcher is interested in determining the proportion of first year university students who have suffered hearing
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Suppose a single die is rolled once. You win $5 if a 1 or a 3 comes up, win $12 if a 5 comes up and lose $10 if a 2, 4, or 6 come up. What does the expected value tell you about the game?
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