1. A particularly common question in the study of wildlife behavior involves observing contests between “residents” of a particular area and “intruders.” In each contest, the “residents” either win or lose the encounter (assuming there are no ties). Observers might record several variables. Which of the following variables is categorical?
A) the number of animals involved in the contest.
B) how long the “intruder” lives in the area before it is accepted as a “resident.”
C) whether the “residents” win or lose.
D) the total number of contests won by the “residents.”
E) the duration of the contest (in seconds)
2. The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61?
(A) 35(B) 61(C) 95(D) 190
3. Which one of the following would be the correct interpretation if you have a z-score of -3.0 on an exam?
A) It means that you missed three questions on the exam.
B) It means that you got three times as many questions wrong as the average student.
C) It means that your grade was three points lower than the mean grade on this exam.
D) It means that your grade was in the bottom 3% of all grades on this exam.
E) It means that your grade is three standard deviations below the mean for this exam.
4. The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark (rounded to the nearest whole number) that a student can have and still be awarded a passing grade?
A) 3.B) 57.C) 40.D) 44.E) 62.
5. Which of the following statements about the correlation coefficient is true?
A) The correlation coefficient measures the proportion of variability between the two variables.
B) The correlation coefficient will be equal to 1 only if all the data lie on a perfectly horizontal straight line.
C) The correlation coefficient measures the fraction of outliers that appear in a scatterplot.
D) The correlation coefficient has no unit of measurement and must always lie between –1 and 1, inclusive.
E) The correlation coefficient equals the proportion of times two variables lie on a straight line.
6. In an attempt to reduce repeat offenders, the Department of Traffic Safety wants to randomly select 5 drivers, without replacement, from a population of 50 drivers convicted of speeding in order to try a new intensive program. The following line is from a random number table:
223684657325595853933099589198279825340193965340955266619174
Which one of the following represents the sample of 5, starting from the left end of the table?
A) 22, 36, 8, 46, 32B) 22, 46, 25, 30, 27C) 22, 36, 25, 30, 27
D) 22, 36, 46, 32, 39E) 22, 23, 36, 46, 32
7. Many people have trouble falling asleep. Researchers wish to determine if a new drug will help these sleep sufferers. To determine if the new medication is more effective than two of the sleep-inducing products currently on the market, the researchers use 140 volunteers who report having trouble sleeping. Sixty of the volunteers are randomly assigned to the new drug, and 40 each to the other two sleep inducing products. Forty-one of the adult volunteers using the new drug report a significant reduction in their inability to fall asleep. What are the experimental units in this study?
A) The 140 volunteers
B) The 60 volunteers who received the new drug.
C) The 19 volunteers who report that they did not achieve a significant reduction in their inability to sleep.
D) The 41 volunteers who report a significant reduction in their inability to sleep.
E) All sleep sufferers.
8. A newspaper wants to determine the level of support in a large town regarding the construction of a new library in a downtown location. Which one of the following would represent a stratified sampling method?
A) Randomly select four residential blocks in the town and ask everyone who lives on those blocks.
B) Select every fourth person who enters the current library until the desired number of people is selected.
C) Take an SRS of people from the city phone directory
D) Take a random sample of residents from each of the northwest, northeast, southwest, and southeast quadrants of the city.
E) Number the residents of the town using the latest census data. Use a random number generator to pick the sample.
9. A local dealer has two video stores in a town, one located on Foothill Drive and the other one on Grand Avenue. The Foothill Drive store does 70% of the dealer’s business in the town, and the Grand Avenue store does the rest. In the Foothill Drive store, 40% of all rentals are DVDs. At the Grand Avenue store, 30% of all rentals are DVDs. If a customer is selected at random, what is the approximate probability that the customer rented a DVD?
A) 0.175B) 0.33C) 0.35D) 0.37E) 0.70
10. A fast-food establishment has many different products for sale. Suppose that 60% of all customers order a hamburger of some kind, 12% purchase a milkshake, and 5% order both. If a customer is randomly selected, what is the probability that he or she ordered neither a hamburger nor a milkshake?
A) 0.05B) 0.28C) 0.33D) 0.48E) 0.60
11. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3.
P(A or B) is
A) 0.6B) 0.3C) 0.09D) 0.51E) 0.33
12. On a recent state bar exam, 22% of the test takers passed the test. 60% were first-time test takers. If 78% of those who passed the test were first-time test takers, what is the probability that a person chosen at random who took the test was either a first-timetest taker or one that passed the test?
A) 82%B) 4%C) 65%D) 35%E) 68%
FREE-RESPONSE
1. A study to determine whether ice cream consumption depends on the outside
temperature (°F) gave the results listed below.
Temperature Pints per Person___
56° 0.386
63° 0.374
69° 0.425A. Sketch a scatterplot and label the axes.
65° 0.406B. Find the equation of the LSRL?
61° 0.344C. Interpret the slope in context to the problem.
47° 0.327D. Interpret r2 in context to the problem.
32° 0.288E. Find and interpret the residual for a temperature
24° 0.269 of 32ºF.
28° 0.256
32° 0.298
40° 0.329
63° 0.381
72° 0.381
2. The table below summarizes 272 employee applications. Some were handwritten and
some were typed. Some contained mistakes and some didn’t.
Mistakes No Mistakes Total
Typed 38 66 104
Handwritten 122 46 168
Total 160 112 272
M = Mistakes N = No MistakesT = TypedH = Handwritten
Use the table above to complete the following.
A. P(M) = B. P(H) = C. P(T|M) =D. P(H U M) =E. P(T and H) =
3. A drug manufacturer is studying how a new drug behaves in patients. Investigators compare two doses: 5 milligrams and 10 milligrams. The drug can be administered by injection, by a skin patch, or by intravenous drip. Concentration in the blood after 30 minutes may depend both on the dose and on the method of administration.
a. Identify the factors and response variables in this experiment.
b. What are the experimental units?
c. Explain how randomization should be used in the design of this experiment.
d. The investigators might be concerned that the drug will behave differently in males and females. What can you use in the design of this experiment to attempt to eliminate the confounding variable of gender.