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		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

 

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		Placebo Group
90		87
65		66
70		76
80		76
30		32
55		44

 

 

 

 

 

 

 

 

 

(Assume that the underlying populations are normally distributed, with equal variances.)  Conduct the appropriate t-test, at a = .05, to determine whether drinking Liquid Braino can improve a person’s memory. Once again...MAKE SURE THAT YOU PICK THE CORRECT HYPOTHESIS TEST!

 

Provide the information indicated below:

a) Statistical Hypotheses

b)  Decision Rule

c)  Calculations

d)  Decision

e)  Interpretation

 

3)  [ 3 pts. ]  A consumer group suspects that a large food chain makes extra money by supplying less than the specified weight of 16 oz in its standard “one pound” packages of ground beef.  A random sample of 10 packages yields a mean weight of 14.7 oz, with a calculated standard error of the mean of 0.26 oz. Using this information, do both of the following:

 

a)  Construct a 95% confidence interval.

b)  Interpret your results in the context of the group’s suspicions.

Attachments:

• 1509194029-HW71.doc