Statistics 13, Midterm 1

Transcription

1 Statistics 13, Midterm 1 Name: 1. (1 points) In this question we will consider two different graphical procedures. Answer as completely as you can, but only supply meaningful comparisons data 5 Frequency data (a) The boxplot on the left was drawn using a dataset consisting of 1, points. The histogram on the right is also based on a dataset with 1, points. Could the same dataset have been used to generate both plots? List the important features of one of the plots that are consistent or inconsistent with the other.

2 data Frequency (b) These two plots are again based on 1, points. Could the same data have been used to generate each plot? List the important features of one of the plots that are consistent or inconsistent with the other. data 2. (1 points) Suppose that together with a story on class sizes at universities in the U.S., Yahoo! News posted a survey on its Web site. Respondents were asked to identify their college and then indicate whether or not they felt their classes were overcrowded. Suppose 6 people said they had been or were currently students at UCLA, and among them, 58 thought that classes were overcrowded. (a) Should the administration be alarmed by this fact? What would you say to calm the Chancellor? (Be specific, don t just write down terms related to surveys.)

3 (b) The Yahoo! poll may not be the best source of student opinions at UCLA. Describe a survey that would better assess how students feel about their class sizes. Indicate how you would address issues like selection bias and nonresponse bias. 3. (5 points) What are the median and the interquartile range? As numerical summaries of a dataset, what do they describe? 4. (25 points) During a polygraph test (also known as a lie detector test), an examinee is asked a series of yes/no questions. The truthfulness of each answer is judged according to various physiological reactions that accompany the examinee s response. According to some theories, a deceptive response to a question causes a reaction (such as the fear of getting caught) that changes a person s respiration, heart rate, blood pressure and skin conductance relative to what they were before the question was asked. A central issue in the dispute over the validity of polygraph testing is how to interpret these physiological changes. How strong must a response be to indicate that the examinee is not being truthful? Depending on how much of a reaction is required, a test is said to be either suspicious or friendly (suspicious meaning it doesn t require much of a reaction to decide that a person is lying; and friendly in the sense that the examiner has to see a very strong reaction before deciding a person has lied). Suppose that the Department of Homeland Security uses lie detector tests in the prosecution of suspected spies. Note that these tests are only used if the suspect claims to be innocent;

4 if they admit to spying there is no need to administer the test. Below we present a pair of two-by-two tables that describe the performance of a suspicious and a friendly lie detector test used to identify spies. The setup for each table is the same: The examinee is asked whether or not they are a spy, and in each case they respond No. The labels spy and not spy refer to whether or not an individual is actually a spy. The labels failed and passed refer to the lie detector test. Failing the test might be used as evidence that the examinee was lying when they said they denied being a spy. The two tables below describe what happens when the test is given to a population of people suspected of spying. Suspicious Test spy not spy failed test.4.8 passed test.1.42 Friendly Test spy not spy failed test.1.19 passed test (a) What is the probability that someone in this population is actually a spy? Verify that this is the same for both tables. (Recall that the Dept. of Homeland Security is only giving the tests to suspected spies; this explains the high probability of spying.) Also, compute the probability that someone in this population fails each test. Does the naming of the tests as friendly and suspicious make sense? (b) The sensitivity of the polygraph test is defined to be the conditional probability that a person will fail a test given that they are in fact a spy. Compute the sensitivity for both the friendly and the suspicious style of test. (c) The specificity of the polygraph test is defined to be the conditional probability that a person will pass the test given that they are not a spy. Compute the specificity for both the friendly and the suspicious style of test.

5 (d) How do the friendly and suspicious styles of testing compare in terms of their specificity and sensitivity? (e) For each style of test, compute the chance that someone is really a spy given that they have failed the test. (f) Which style of test would you recommend for use by the Department of Homeland Security for screening suspected spies? Why? (g) Overcome by a sense of patriotism, suppose that Krispy Kreme Corporation decides to give these two kinds of tests to all of its new employees as part of their pre-employment screening process. In this population, the probability that someone is a spy is only.1. Assume again that everyone who is asked whether or not they are a spy answers No. (Anyone admitting to being a spy would not be hired and hence would not be subjected to the test.) Assuming the specificity and sensitivity of the friendly and suspicious tests remain the same, fill in the two tables below. Suspicious Test failed test passed test spy not spy failed test passed test Friendly Test spy not spy

6 (h) For each of the two testing approaches, compute the chance that a job candidate fails the lie detector test. (i) For each style of test, compute the chance that someone in this population of job candidates is really a spy given that they have failed the test. (j) What impact has the change in the prevalence of espionage made in the performance of the two tests? Which test would you recommend that Krispy Kreme use for screening its job candidates? Why?