# In the magical realm ruled by King Arthur, there has recently been an alarming increase

August 30, 2017

Question
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:

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DRAGON

WITH PILLS

NO PILLS

Trogdor

88

95

Smaug

41

44

Gojira

33.5

34

Gamera

63

68

Godzilla

87

90

Mekagojira

34

40

Fred

81

90

Tiamat

43

44

Dr. Lizardo

7

5

Conduct the appropriate t-test, at a = .05, 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!

Provide the information indicated on the following page.

Provide the following information for the problem on the previous page:

a) Statistical Hypotheses

b) Decision Rule

c) Calculations

d) Decision

e) Interpretation

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