ECO 380 – Quantitative Critical Thinking Dr. Wesley Pech

First Exam October 21, 2016

(12 points) 1. The chart below shows the breakdown of votes by education for each candidate in the South Carolina Republican Primary in February 2016. The percentage of total votes received by each candidate was the following:

Trump – 32.5% Rubio – 22.5% Cruz – 22.3% Bush – 7.8% Kasich – 7.6% Carson – 7.2%

Given this information, answer the following questions:

a) Why do the percentages for each candidate add up to 100%? b) Why don’t the percentages for each education level add up to 100%? c) If only voters with a post graduate degree could have voted, who would have won the primary? Explain. d) Were there more voters with a high school degree or with a post graduate degree? Explain.

(10 points) 2. Suppose the Weather Channel gives the following probability of precipitation for each day for a hypothetical week:

Monday – 10% Tuesday – 20% Wednesday – 30% Thursday – 40% Friday – 50%

a) What is the probability that will rain either Thursday or Friday? b) What is the probability that will rain both on Tuesday and on Wednesday?

(10 points) 3. In April 2009, a resident of Lake Bowen here in Spartanburg County was in the local news for a peculiar reason: she wanted a cheese toast snack, but to her surprise, the toaster popped up a toast that had the image of Jesus on it. According to her, “I know there’s a lot of people who believe there’s some divine reason for it being there…I just don’t know, but I could never eat it.” How should a critical thinker analyze this case? (12 points) 4. In a recent issue of the Old Gold and Black, there was an article about the decline in SAT scores here at Wofford. Consider the following quote: In 2015, the middle fifty percent range fell between 1080 and 1260. The middle fifty percent is defined here as the interval between the 25th and 75th percentiles. Given this information, answer the following questions: a) Is the median SAT score at Wofford necessarily within the interval above? Explain. b) Is the average SAT score at Wofford necessarily within the interval above? Explain. c) Is the modal SAT score at Wofford necessarily within the interval above? Explain.

(10 points) 5. Suppose a person is interested in knowing the caloric content of different types of food. In order to rank the foods from most to least caloric, this person checks the nutritional information given by the producer and calculates the number of calories per gram that the product has. Call this variable the ‘caloric factor.’ For example: 20 grams of sugar have 80 calories. This means that sugar has 4 calories/gram, so its caloric factor is 4.

Now let’s take the case of peanut butter. One brand says that 33g of peanut butter has 190 calories.

Given all this information, answer the following questions: a) What is going to happen to the caloric factor of peanut butter if we start adding sugar to it? Justify your answer; b) If we continue to add sugar to peanut butter indefinitely, what is going to happen to its caloric factor? And c) If this person wants to eat as few calories as possible, buthas to choose between 100g of peanut butter or 100g of peanut butter mixed with sugar, which option should he choose? Explain.

(10 points) 6. If an index is being formulated, when should you consider using the geometric mean of the different variables instead of the arithmetic mean?

(6 points) 7. A dataset has an average of 40 and a standard deviation of 6. Given this information, what else can you say about the data?

(20 points) 8. DNA tests have recently become more popular in criminal investigations. Suppose a hair of the murderer was found in the crime scene. The DNA test will always give a match if the actual murderer is tested. If an innocent person takes the test, there is only a 10% chance of a match. There are only three suspects who could have committed the crime: A, B, and C. Given their records, their relationship with the victim, and their alibis, the detective has assigned the following prior probabilities of each suspect being guilty:

A: 60% B: 30% C: 10%

All suspects took the DNA test, and to the detective’s surprise, there was a match for all three suspects. Given this information, and assuming that the detective is a rational Bayesian, answer the following questions:

a) What is the probability of each suspect being guilty now? b) Which suspect(s) benefited from these results? Which one(s) were harmed? Explain the intuition.

(10 points) 9. Recently, there have been several tv shows about mediums. Basically, these people claim that they can make contact with dead people. In Brazil many people have also claimed to possess this capacity. In fact, one of them, Chico Xavier, became so famous in Brazil that movies were made about his life and statues were built in his honor. Xavier’s believers have frequently argued that one piece of evidence in favor of the hypothesis that he really had this power is that he provided this ‘service’ free of charge. If he is not seeking wealth by doing this, then it must be true. Critically analyze this argument.