Page 1 of 2 Psychology 60, Fall 2016 Name: __________________________________ Homework #7 ID#: __________________________________ Due in class Tuesday, November 22nd Homework must be stapled, legible, and handed in before the beginning of lecture on the date indicated above. If you fail to turn in a homework, or turn it in late, you will receive zero points. For computation problems, use the computation formulas, not the definition formulas. Show all of your work, including the symbolic versions of any formulas that you use to derive your answers, round all intermediate and final results out to exactly 2 decimal places, and draw a box around your final answer. 1) [ 7 pts. ] In the magical realm ruled by King Arthur, there has recently been an alarming increase in the number of knights and princesses eaten by fire-breathing dragons. There is, of course, concern that this high-fat diet will result in increased levels of heart disease among the kingdom's dragons. To counter this growing health risk, Merlin the Magician has developed special diet pills for dragons. He swears that dragons that eat the pills immediately before a meal will subsequently eat fewer knights and princesses. Because you are the most respected professor of numerology at the University of Camelot in South Devonshire (UCSD), King Arthur hires you to test Merlin's claim. You randomly select 9 fire-breathing dragons, and the number of knights and princesses eaten by each dragon is measured twice: once when the dragon has eaten Merlin's pills prior to a meal (\"WITH PILLS\"), and once when the dragon has not eaten these pills prior to a meal (\"NO PILLS\"). (Assume that appropriate counter-balancing is employed, and that all necessary assumptions for the appropriate hypothesis test have been met.) The number of knights and princesses that each dragon ate in each condition is listed below: DRAGON Trogdor Smaug Gojira Gamera Godzilla Mekagojira Fred Tiamat Dr. Lizardo WITH PILLS 88 41 33.5 63 87 34 81 43 7 NO PILLS 95 44 34 68 90 40 90 44 5 Conduct the appropriate t-test, at , to determine whether dragons eat fewer knights and princesses when they have consumed Merlin's diet pills prior to a meal. MAKE SURE THAT YOU PICK THE CORRECT HYPOTHESIS TEST! Spending at least a little time making sure that you understand exactly when and why a particular type of test would be appropriate can save you a lot of wasted effort! Start with the hypotheses and proceed through interpretation. Page 2 of 2 2) [ 7 pts. ] The makers of the Liquid Braino brand energy drink claim that their product contains special ingredients that can improve a person's memory. To test this claim, a public interest organization randomly selected 12 individuals, and then randomly assigned each of these individuals to one of two possible groups: i. The experimental group ("Braino Group"), in which each subject drank a case of Liquid Braino. ii. The control group ("Placebo Group"), in which each subject drank a case of a soda that looked and tasted exactly like Liquid Braino, but did not contain any of Liquid Braino's special ingredients. (No subjects knew which type of drink they had been given.) Later, all subjects were given a memory test, in which higher scores indicate better memory. The scores earned by the subjects in each group are listed below: Braino Group 90 65 70 80 30 55 Placebo Group 87 66 76 76 32 44 (Assume that the underlying populations are normally distributed, with equal variances.) Conduct the appropriate t-test, at , to determine whether drinking Liquid Braino can improve a person's memory. Once again...MAKE SURE THAT YOU PICK THE CORRECT HYPOTHESIS TEST! Start with the hypotheses and proceed through interpretation. 3) [ 3 pts. ] A university wants to estimate the mean temperature in a lecture hall. They measure the temperature at random times of day over a two week period. Results: n = 50, sample mean = 74, and s = 3.2. a) Construct a 95% confidence interval and express the interval as an inequality. b) Interpret your results in language