Sample questions for Exam 3

Warning As a supplement to the additional test of significance problems listed under Unit 11, the questions provided below are meant to give you a sense of the type of material that you may face on the last exam. You should not infer that the exam will look exactly like the sample provided or that only similar questions may be used.

At the bottom of this page, you'll find a list of things you should be able to do based on the material offered in during the semester.

Problem One hospital has 218 single live births during the month of January. Another has 536. Which is likelier to have 49% or fewer male births? Or is it equally likely? Explain your response in at most five sentences. [There is about a 52% chance for a single live-born infant to be male.] [Ans: The hospital with 218 single births has the greater likelihood of 49% or fewer male births.]

Problem According to an article in the 28 November 1990 edition of the San Francisco Chronicle, 74% of the freshman at UC Berkeley scored over 500 on the verbal section of the SAT. If the verbal SAT scores for the entire class have an SD of 80 points and follow a normal distribution, what is the average score for this group? [Ans: The average is approximately 556.]

Problem Smokers have about three times the death rate from cirrhosis as non-smokers, adjusting for age and sex. However, alcohol consumption is a confounding variable. This means that

(i) Alcohol causes cirrhosis.
(ii) Drinking is associated with smoking and alcohol causes cirrhosis.

Choose one option and justify your choice in at most three sentences.

Problem There are about 2700 institutions of higher learning in the United States. In 1976, as part of a continuing study of higher education, the Carnegie Commission took a simple random sample of the institutions. The average enrollment in the 225 sample schools was 3700, with an SD of 6000. A histogram for the enrollments was plotted and did not follow the normal curve. However, average enrollment at all 2700 institutions was estimated to be around 3700 give or take 400 or so. Say whether each of the following statements is true or false, and explain why in at most three sentences.

(i) It is estimated that 95% of the institutions of higher learning in the US eroll between 2900 and 4500 students. [False]
(ii) An approximate 95% confidence interval for the average enrollment of all 2700 institutions runs from 2900 to 4500. [True]
(iii) If someone takes a simple random sample of 225 institutions of higher learning, and goes two SE's either way from the average enrollment of the 225 sample schools, there is about a 95% chance that the interval will cover the average of all 2700 schools. [True]
(iv) The normal curve can't be used to figure the confidence interval here at all because the data doesn't follow the normal curve. [False]

Problem For the men aged 25-34 in the HANES study, the relationship between education [years of schooling completed] and systolic blood pressure can be summarized as follows:

Average education = 13 years	SD = 3 years
Average BP = 124 mm	SD = 14 mm	r = -0.1

(i) Find the rms error of the regression line for predicting blood pressure from education. [Ans: Approximately 13.9 mm]
(ii) Predict the blood pressure of a man with 14 years of education. [Ans: Approximately 123.5 mm]
(iii) This prediction is likely to be off by ____ mm or so. Or can this be determined from the information given? [See (i)]
(iv) Of men with 10 years of education, estimate the percentage who have a blood pressure of 124 mm or higher. [Ans: Approximately 54%]

Problem A fair die is rolled twice. Find the probability that a "six" comes up on one roll, but not both. [Ans: 5/18]

Problem A coin is tossed 10 times. Find the probability of getting exactly 6 heads or exactly 6 tails. [Ans: 2(10,6)(0.5)^10]

Problem In 1969, Dr Spock [author of a very famous child-rearing book] came to trial before Judge Ford in Boston's federal court house. The charge was conspiracy to violate the Military Service Act. "Of all defendants, Dr. Spock, who had given wise and welcome advice on child rearing to millions of mothers, would have liked women on this jury." [FPP, A-30] The jury was drawn from a panel of 350 people selected by the court clerk. This panel included only 102 women even though the majority of the eligible panel members were women. How likely is it that 350 people chosen at random from a population which is 50% women would include 102 or fewer women? [Ans: P(W < 102) = 0.] What can you conclude about the clerk's selection?

You should be able to do any of the following:

Understand the use of treatment and control groups
Identify design problems with a double-blind methodology in a given experimental scenario
Identify the most appropriate experimental design and analysis for a given situation
Identify a percentile rank from a frequency table of data
Provide and/or interpret the information contained in a box and whisker plot
Determine a percentile value through normal approximation using a reported average and SD
Interpret information contained in a two-variable scatter plot
Use a regression line analysis to find a predicted value with error measure
Discuss how a residual plot can be used to 'detect' [non-]linear association
Compute probabilities using the 'Not,' 'Addition' and 'Multiplication' Rules as well as the Binomial Formula
Create and interpret a confidence interval in context
Decide on an appropriate test of significance methodology for a given scenario
Perform an appropriate test of significance for a given scenario
Interpret a P-value in the context of a test of significance
Discuss / critique the appropriateness of a particular test of significance in context
Discuss the difference(s) between a t-curve and the normal curve