Stat 217 - HW 2

Due Beginning of class Wednesday, Jan. 20

Note change in syllabus on due date: You can turn in Tuesday but you also have the option of asking questions in class on Tuesday and then turning in on Wednesday. There will probably not be a pre-lab due Thursday.

1) (2 pts) Take the “Learning Styles Survey” – you can access it under the Assignments tab in Blackboard, then Surveys, then Learning Styles survey. Then follow the link in the Instructions box to access the survey. (You can right-click on the link that opens the survey and ask it to open the file in a new window if you want). Once you complete the survey, enter the numerical scores it gives you for each scale in the Blackboard page. Don’t worry about the score Blackboard gives you on this survey, we will note whether or not you completed it when we grade the homework assignment.

2) (Topic 4, 10 pts) For each research question below:

(i) Identify the observational units and variable of interest

(ii) Identify the population of interest

(iii) Describe in words the parameter of interest

(iv) Specify a sampling frame (p. 34) you could use (e.g., list of all registered students at Cal Poly) to select a random sample from the population and briefly outline the sampling method you would use.

(a) Estimate the average number of words on a page of a history textbook.

(b) Do a majority of Cal Poly professors classify themselves as liberals?

(d) Do college freshmen really tend to gain an average of 15 pounds during their first term at college?

3) Activity 5-14 (p. 86) – 10 pts

4) (Topics 4 and 5, 7 pts) Under course materials, click the link for Videos and then play the second video “Will you hold my hand?” This video describing a previous Stat 217 project can be found on youube: http://www.youtube.com/watch?v=pjZ52w1c34I (or search on Wanna Hold My Hand Cal Poly or go to Course Materials > Videos in Blackboard). Watch the video and then:

(a) Identify the observational units and response variable (and classify the response variable as quantitative or categorical).

(b) Though not explicitly shown in this study, suggest an explanatory variable that the researchers could actively impose on the subjects in this study.

(c) Explain the difference between random sampling and random assignment in this study by giving an example of how each could be implemented.

(d) To what population are you willing to generalize the results of their study? Briefly justify your choice.

5) (Topic 6, 6 pts) The ELISA test for AIDS was used in the screening of blood donations in the early 1990s. As with most medical diagnostic tests, the ELISA test is not infallible. If a person actually carries the AIDS virus, experts estimate that this test gives a positive result 97.7% of the time. (This number is called the sensitivity of the test.) If a person does not carry the AIDS virus, ELISA gives a negative result 92.6% of the time (the specificity of the test). Recent estimates are that 0.5% of the American public carries the AIDS virus (the base rate with the disease). What we will explore below is if a randomly selected member of the U.S. population tests positive, how often does that person actually carry the virus…

(a) Make a conjecture (free point!) as to the proportion of positive tests that correctly identify someone with AIDS (If you test positive, what is the likelihood you have the disease).

Below is a two-way table representing 1,000,000 people.

	Positive test	Negative test	Total
Carries AIDS virus	(2)	(2)	(1)
Does not carry AIDS	(3)	(3)	(1)
Total	(4)	(4)	1,000,000

(b) Let’s calculate the proportion of positive tests that have the AIDS virus:

(1) Based on the recent estimates of someone carrying the AIDS virus, fill in the row totals. Hint: Assuming that .5% of the population of 1,000,000 people carries AIDS, how many such carries are there in the population? How many noncarriers?

(2) For the people with the AIDS virus, based on the sensitivity of the ELISA test, how many will test positive and how many will test negative? Fill in these values in the table.

(3) For the people without the AIDS virus, based on the specificity of the ELISA test, how many will test positive and how many will test negative? Fill in these value in the table.

(4) Now determine the column totals.

Now calculate from the table the proportion of people with positive tests that actually carry the aids virus.

(d) Calculate and interpret the relative risk of having the AIDS virus for someone with a positive test compared to someone with a negative test. Hint: You will have to do one more calculation from the table first.