Practice Midterm Solutions
I. Short answer questions
1. A stemplot of a set of data is roughly symmetric, but the data do not even approximately
follow the 68-95-99.7 rule. We conclude that the data are
A) Normal, but they are not standard normal.
B) Standard normal.
D) Not enough information to determine whether it is standard normal.
2. A high school guidance counselor wants to study the later earnings of the class of 1990.
The high school had 800 graduates in the class of 1990; among them, 400 obtained
college degrees and the other 400 did not. In the year 2000, the counselor randomly
selects 20 individuals from among those who obtained college degrees, and another 20
individuals among those who didn’t obtain college degrees. Earnings data is collected
on these 40 selected individuals. This study is:
A) A designed experiment, in which the “treatment group” receives a college degree, and
the “control group” gets no college degree.
B) Based on “anecdotal evidence”, and hence is not reliable.
C) An observational study, in which the 40 selected individuals are a Simple Random
D) An observational study. However, the 40 selected individuals are not a Simple Random
3. Following the previous question. From the data collected, the high school guidance
counselor finds that the average earnings of the 20 individuals who didn’t obtain college
degrees is $23,000. The value $23,000 is
B) a statistic for the sample.
C) a statistic for the population.
D) none of the above
4. There are three children aged 3, 4, and 5 in a room. If another 4-year-old child enters the
room, what will happen to the mean and variance?
A) The mean will stay the same but the variance will increase.
B) The mean will stay the same but the variance will decrease.
C) The mean and variance will both stay the same.
D) The mean and variance will both decrease.
Answer: B 5. The average salary of all female workers is $35,000. The average salary of all male
workers is $41,000. What must be true about the average salary of all workers?
A) It must be $38,000.
B) It must be larger than the median salary.
C) It could be any number between $35,000 and $41,000.
D) It must be larger than $38,000.
6. A set of midterm exam scores has a median that is much larger than the mean. Which
of the following statements is most consistent with this information?
A) A stemplot of the data would be symmetric.
B) A stemplot of the data would be skewed left.
C) A stemplot of the data would be skewed right.
D) The data set must be so large that it would be better to draw a histogram rather than a
Topic: 1.2 Describing Distributions with Numbers
7. Which of the following is likely to have a mean that is smaller than the median?
A) The salaries of all National Football League players.
B) The scores of students (out of 100 points) on a very easy exam in which most score
perfectly, but a few do very poorly.
C) The prices of homes in a large city.
D) The scores of students (out of 100 points) on a very difficult exam on which most score
poorly, but a few do very well.
Topic: 1.2 Describing Distributions with Numbers
Use the following density curve to answer questions 8 -10:
0 0.5 1.0 1.5 2.0 X 8. Determine whether each of the following statements regarding this density curve is true
A) It is symmetric.
B) The total area under the curve is 1.
C) The median is 1.
D) The mean is 1.
Answer: A) True, B) True, C) True, D) True
9. For this density curve, what percent of the observations lie above 1.5?
10. For this density curve, what percent of the observations lie between 0.5 and 1.2?
Use the following to answer questions 11 and 12:
Volunteers for a research study were divided into three groups. Group 1 listened to
Western religious music, group 2 listened to Western rock music, and group 3 listened to
Chinese religious music. The blood pressure of each volunteer was measured before and
after listening to the music, and the change in blood pressure (blood pressure before
listening minus blood pressure after listening) was recorded.
11. What could we do to explore the relationship between type of music and change in
A) See if blood pressure decreases as type of music increases by examining a scatterplot.
B) Make a histogram of the change in blood pressure for all of the volunteers.
C) Make side-by-side boxplots of the change in blood pressure, with a separate boxplot for
D) Do all of the above.
Answer: C 12. A scatterplot of change in blood pressure versus the type of music listened to is given
Change in blood pressure
Western Chinese Western
religious religious rock
Type of music
What do we know about the correlation between change in blood pressure and type of
A) It is negative.
B) It is positive.
C) It is first negative then positive.
D) None of the above.
Answer: D 13. Which histograms display a sampling distribution that is unbiased for estimating the
proportion of women at a large university, which is known to be 45%? (make sure you
point out ALL histograms that suggest an