Answer "true" or "false" to the following statements. (5pts)

For the following story, tell me (1) if the reasoner is plausibly seen as employing a judgment heuristic (2) if a judgment heuristic is being used what judgment heuristic the reasoner is likely using. (4pts)

6.) Mike Lake, a  member of the Canadian Parliament, has proposed legislation to add Sasquatch (aka Bigfoot) to the Canadian Species at Risk Act.  Part of the petition reads, "the debate over their (Bigfoot's) existence is moot in the circumstance of their tenuous hold on merely existing."  Apparently  the lack of sightings, while seeming to undermine probability that  Bigfoot exists, is seen by some (like "Bigfoot" researcher Todd Standing) as increasing the probability that the species is existent but endangered.

(1) Yes a heuristic is likely being used.

(2) The legislation seems to represent a case of belief perseverance.  Specifically, the proposed legislation seems to represent a resistance by individuals like Mr. Lake and Mr. Standing to modifying or rejecting their belief in the existence of Bigfoot in light of a paucity of sightings. 

Use Probability Theory to Solve the Following Problem. Make Sure to Show Your Work. (6 Pts)

                                               P(A₁) x P(B given A₁)
P(A₁ given B) = -------------------------------------------------------------
                                [P(A₁) x P(B given A₁)] + [P(A₂) x P(B given A₂)]


Given two urns one with two red and three white balls and the other with three pink, two yellow and four red balls.  If one draws a ball from each urn, estimate the probability of the following outcomes:

10.) Two white.

P(2W) = P(W_u1) and P(W_u2)

These events are independent, so use the restricted conjunction rule.

P(2W) = P(W_u1) and P(W_u2) = P(W_u1) x P(W_u2)

P(W_u1) is simple events that fall under the principle of indifference, so use the classical theory to estimate its probability

P(W_u1) = #W/total # of balls = 3/5

P(W_u2)  is simple events that fall under the principle of indifference, so use the classical theory to estimate its probability

P(W_u2) = #W/total # of balls = 0/9


P(2W) = P(W_u1) and P(W_u2) = P(W_u1) x P(W_u2) = 3/5 x  0 = 0


11.) A white and a yellow or a pink.

P(1W and (1Y or 1P) = P(W_u1) and P(Y_u2 or P_u2)

P(W_u1) is simple events that fall under the principle of indifference, so use the classical theory to estimate its probability

P(W_u1) = #W/total # of balls = 3/5

P(Y_u2 or P_u2) is a disjunction where the favorable outcomes are mutually exclusive, so use the restricted disjunction rule.

P(Y_u2 or P_u2) = P(Y_u2) + P(P_u2)

P(Y_u2) is simple events that fall under the principle of indifference, so use the classical theory to estimate its probability

P(Y_u2) = #Y/total # of balls = 2/9

P(P_u2) is simple events that fall under the principle of indifference, so use the classical theory to estimate its probability

P(P_u2) = #P/total # of balls = 3/9
 

P(1W and (1Y or 1P) = P(W_u1) and P(Y_u2 or P_u2) = P(W_u1) x P(Y_u2 + P_u2) = 3/5 x  (3/9 + 2/9) =  3/5 x 5/9 = 15/45 = 1/3
 

12.) After winning only 4 out of 10 games last year, Coach Hoax vows to double the number of games won this year.  At the end of this years season, the record is 5 out of 10.  Coach Hoax announces the he has been 63% successful (5/8).


Coach hoax promised to increase the number of games by 4.  He increased the number of games by 1.  Hence, he was only 25% successful.


13.) As evidence that Americans are wasteful Cidel Fastro notes that the average daily beer consumption in America is 1.2 beers.  He notes that, "Only wasteful people like Americans would drink 20% of a beer and then leave the rest every day!!!"

Castro falsely equates average per day with actual consumption per day to get a beer only 20% consumed each day.



14.)  In order to find out how many people think the soundtrack for MI-2 is good, Time-Warner conducted a survey of  1,000 randomly selected people.  65% said that they liked the soundtrack.  Therefore, Johnny Yesmann, executive vice president of the sound track division concluded that exactly 65% of the real world population thinks that the sound track is good.

JY should conclude that in the actual world, the percentage of people who liked the soundtrack was 95% likely to fall within the range of  65% plus or minus the margin of error (± 4 percentage points).



This section will appear on your tests only if your class completed the lectures on section 9.5

Use Your Knowledge of Scientific Method to Criticize the Following Argument (4pts):

15.) In a survey of 100 "A" students, 70% reported drinking caffeinated beverages.  Based upon this result, we can conclude that drinking caffeinated beverages is a causal factor in getting As.

This is a descriptive study that only provides correlational evidence.    Such evidence can only support a causal inference if the data is carefully analyzed to rule out other potential causes.  The best type of study would be a double-blind placebo-controlled study.



 

This section will appear on your tests only if your class completed the lectures on section 9.2
Identify the type of causal relationship in the example and state which of the five of Mill's methods the person employed. (4pts)
11.) Wallis wants to know why his two favorite students received different grades of the last exam.  Wallis knows that each student has the same basic logical ability, memory, level of conscientiousness, etc..  Wallis discusses the exam with each person, looking to see if there was any difference between the two students.  Both students studied the same materials for the same amount of time and in the same manner,  Finally, he discovers that the student who received a B only slept 5 hours before the exam, whereas the student who received an A got a full 8 hours of sleep before the exam.  Therefore, since he can find no other differences between the students, Wallis concludes that lack of sleep caused the grade difference.

Wallis employed the method of differences in examining two cases to discover a single factor in which they differed.  The method of differences is used to find a sufficient cause.  Hence, Wallis' inference was that a lack of sleep was sufficient to cause the grade difference.