Practice Exam for Midterm II (Spring 2001)
1.X and Y are two categorical variables. The best way to determine if there is a relation between them is to
A)calculate the correlation between X and Y.
B)draw a scatter plot of the X and Y values.
C)make a two-way table of the X and Y values.
D)all of the above.
2. A business has two types of employees: managers and workers. Managers earn either $100,000 or $200,000 per year. Workers earn either $10,000 or $20,000 per year. The number of male and female managers at each salary level and the number of male and female workers at each salary level are given in the two tables below.
Managers Workers
MaleFemale Male Female
$100,0008020 $10,000 30 20
$200,0002030 $20,000 20 80
The conditional distribution of the salary (S) of an employee, given that the employee
is a male is:
A)
S / 10,000 / 20,000 / 100,000 / 200,000P(.) / .6 / .4 / .8 / .2
B)
S / 10,000 / 20,000 / 100,000 / 200,000P(.) / .2 / .133 / .533 / .133
C)
S / 10,000 / 20,000 / 100,000 / 200,000P(.) / .167 / .333 / .333 / .167
D)
S / 10,000 / 20,000 / 100,000 / 200,000P(.) / .1 / .067 / .267 / .067
- A study of the salaries of full professors at Upper Wabash Tech shows that the median salary for female professors is considerably less than the median male salary. Further investigation shows that the median salaries for male and female full professors are about the same in every department (English, physics, etc.) of the university. This apparent contradiction is an example of
A)extrapolation.
B)Simpson's paradox.
C)causation.
D)correlation.
4. When possible, the best way to establish that an observed association is the result of a cause and effect relation is by means of
A)the least-squares regression line.
B)the correlation coefficient.
C)a two-way table.
D)a well-designed experiment.
5.If changes in an explanatory and a response variable are caused by changes in a lurking variable, any observed association between the explanatory variable and the response variable is due to
A)a cause-and-effect relation between the explanatory and response variables.
B)common response.
C)confounding.
D)correlation.
6.Recent data show that states that spend an above-average amount of money X per pupil in high school tend to have below-average mean Verbal SAT scores Y of all students taking the SAT in the state. In other words, there is a negative association between X and Y. This is particularly true in states that have a large percentage of all high school students taking the exam. Such states also tend to have larger populations. The most plausible explanation for this association is
A)X causes Y. Overspending generally leads to extra, unnecessary programs, diverting attention from basic subjects. Inadequate training in these basic subjects generally leads to lower SAT scores.
B)Y causes X. Low SAT scores creates concerns about the quality of education. This inevitably leads to additional spending to help solve the problem.
C)changes in X and Y are due to a common response to other variables. If a higher percentage of students take the exam, the average score will be lower. Also, states with larger populations have large urban areas where the cost of living is higher and more money is needed for expenses.
D)the association between X and Y is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.
7.A study of human development showed two types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching the different kinds of movies. One kind of movie was shown at 8 A.M. (right after the children had breakfast) and another at 11 A.M. (right before the children had lunch). It was found that during the movie shown at 11 A.M., more crackers were eaten than during the movie shown at 8 A.M. The investigators concluded that the different types of movies had an effect on appetite. The results cannot be trusted because
A)the study was not double-blind. Neither the investigators nor the children should have been aware of which movie was being shown.
B)the investigators were biased. They knew beforehand what they hoped the study would show.
C)the investigators should have used several bowls, with crackers randomly placed in each.
D)the time the movie was shown is a lurking variable.
8.A group of college students believes that herbal tea has remarkable restorative powers. To test their theory they make weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy. Which of the following may be correctly concluded from this study?
A)herbal tea does improve one's emotional state, at least for the residents of nursing homes.
B)there is some evidence that herbal tea may improve one's emotional state. The results would be completely convincing if a scientist had conducted the study rather than a group of college students.
C)the results of the study are not convincing since only a local nursing home was used and only for a few months.
D)the results of the study are not convincing since the effect of herbal tea is confounded with several other factors.
9.In a recent study, a random sample of children in grades two through four showed a significant negative relationship between the amount of homework assigned and student attitudes. This is an example of
A)an experiment.
B)an observational study.
C)the establishing of a causal relationship through correlation.
D)a block design, with grades as blocks.
10.Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. 44 of these volunteers report a significant reduction in their allergy symptoms without any drowsiness. This study could be improved by
A)including people who do not suffer from allergies in the study in order to represent a more diverse population.
B)repeating the study with only the 44 volunteers who reported a significant reduction in their allergy symptoms without any drowsiness, and giving them a higher dosage this time.
C)using a control group.
D)all of the above.
11.One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. The factor in this study is
A)which treatment the volunteers receive.
B)the use of randomization and the fact that this was a comparative study.
C)the extent to which the depression was reduced.
D)the use of a psychiatrist to evaluate the severity of depression.
12.One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. Suppose volunteers were first divided into men and women, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. This would be an example of
A)replication.
B)confounding. The effects of gender will be mixed up with the effects of the drugs.
C)a block design.
D)a matched pairs design.
13.In an experiment, an observed effect so large that it would rarely occur by chance is called
A)an outlier.
B)infuential.
C)statistically significant.
D)bias.
14.The sampling distribution of a statistic is
A)the probability that we obtain the statistic in repeated random samples.
B)the mechanism that determines whether randomization was effective.
C)the distribution of values taken by a statistic in all possible samples of the same size from the same population.
D)the extent to which the sample results differ systematically from the truth.
15 .A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled felt that drinking was a problem among college students. A simple random sample of 50 undergraduates at Ohio State University found that 70% felt that drinking was a problem among college students. The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State is approximately 40,000. Suppose the actual proportion of undergraduates at Johns Hopkins University who feel drinking is a problem among college students is 70%. The mean of the sampling distribution of the percentage that feel drinking is a problem in repeated simple random samples of 50 Johns Hopkins undergraduates is
A)50%.
B)60%.
C)65%.
D)70%.
16.In a particular game, a six faced die is tossed. The die is such that the likelihood of a face is proportional to the number on the face. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. If it costs you $1 to play the game, the probability that you win more than the cost of playing is
A)1/2.
B)1/6.
C)6/21.
D)15/21.
17.Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint then the following must be true:
A)A and B must be independent
B)The complement of A and complement of B are disjoint
C)The complement of A and complement of B are independent
D)A and B are not independent
18.For an unfair coin it is known that P(H) = 2/3 and P(T) = 1/3. The coin is tossed repeatedly. Which of the following run is least likely:
A)TT
B)HHH
C)HHHH
D)HHHHH
19.Ignoring twins and other multiple births, assume babies born at a hospital are independent events, with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. The probability that at least one of the next three babies is a boy is
A)0.125.
B)0.333.
C)0.75.
D)0. 875.
20. Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. Let X be the total of the two balls selected. Which of the following is the correct set of probabilities for X.
(A)
X / 1 / 2 / 3P(.) / 1/3 / 1/3 / 1/3
(B)
X / 3 / 4 / 5P(.) / 1/3 / 1/3 / 1/3
(C)
X / 1 / 2 / 3P(.) / 1/6 / 2/6 / 3/6
(D)
X / 3 / 4 / 5P(.) / 1/6 / 2/6 / 3/6
21. Let the random variable X be a random number with the uniform distribution on the interval [-2, 1]. The probability that X is either less than –1 or greater than 0.5 is:
(A)1.5
(B)0.5
(C)0.75
(D)Cannot be determined.
22. I roll a pair of fair, four faced dice and compute the number of spots on the two sides facing up. Denote this total by X. The probability that X is at least 7 is
A)15/36
B)21/36
C)2/16
D)3/16
23.A random variable is
A)a hypothetical list of the possible outcomes of a random phenomenon.
B)any phenomenon in which outcomes are equally likely.
C)any number that changes in a predictable way in the long run.
D)a variable whose value is a numerical outcome of a random phenomenon.
24. Suppose X is a continuous random variable taking values between 0 and 2 and having the probability density function below.
Then P(1 < X < 2) has value
A)0.50.
B)0.33.
C)0.25.
D) 0.00.
25.Let X be a continuous random variable. Then which of the following must be true?
A)P(X > 5) = P(X < -5)
B)P(X > 5) = 1 – P(X < 4)
C)P(X= 0) = 1/2
D)P(X > 5) = P(X > = 5)
26.Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. Let X be the total of the two balls selected. The mean of X is
A)2.0.
B)14/6.
C)4.0.
D)26/6.
27.The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random variable with mean 10 ounces and standard deviation 1 ounce. Suppose we pick four tomatoes from the bin at random and put them in a bag. The weight of the bag is a random variable with a standard deviation (in ounces) of
A)0.25.
B)2.0.
C)1.0.
D)4.0.
28.The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random variable with mean 10 ounces and standard deviation 1 ounce. Suppose we pick two tomatoes at random from the bin. The difference in the weights of the two tomatoes selected (the weight of the first tomato minus the weight of the second tomato) is a random variable with a standard deviation (in ounces) of
A)0.00.
B)1.00.
C)1.41.
D)2.00.
29.I toss a fair coin a large number of times. Assuming tosses are independent, which of the following is true?
A)Once the number of flips is large enough (usually about 10,000) the number of heads will always be exactly half of the total number of tosses. For example, after 10,000 tosses I should have 5,000 heads.
B)The proportion of heads will be about 1/2 and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases.
C)As the number of tosses increases, any long run of heads will be balanced by a corresponding run of tails so that the overall proportion of heads is 1/2.
D)As the number of tosses increases, long runs of heads become rarer and rarer.
30.A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.
X / 0 / 1 / 2 / 3 / 4P(.) / 0.1 / 0.1 / 0.1 / 0.1 / 0.6
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is
A)1.4.
B)2.0.
C)3.0.
D)4.0.
31 .In a particular game, a die, for which even faces are twice as likely as odd faces is tossed. If the number of spots showing is either 4 or 5 you win $1, if number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. The expected value of X is
A)$0.00.
B)$1.00.
C)$1.22.
D)$2.50.