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 |
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!
a) Statistical Hypotheses
b) Decision Rule
c) Calculations
d) Decision
e) Interpretation
