Statistics

Name Instructor
Time Limit: 120 Minutes
Any calculator may be used for this exam. Computers, cell phones, or other communication devices
are not allowed. Allowed formulas and tables are attached to the exam. Students may not bring the
own notes, formulas, or tables into the exam.
This exam has two parts:
Part I – 9 Multiple-Choice questions, worth 10 points each (no partial credit)
Part II – 11 Free Response questions, worth 10 points each (partial credit possible)
PART I – Each problem in this section is worth 10 points, and has only one part to each problem. It
is not necessary to show work. Partial credit will not be awarded for incorrect answers. Circle the
best answer available.
1) Medical research often utilizes twins for matched-pairs experiments because of their biological
similarities. If an experimental design uses a coin-toss to decide, within each pair of twins, which
subject will receive a treatment and which will not, which sampling technique is being used to
assign treatment?
a) Systematic Random Sampling
b) Cluster Random Sampling
c) Stratified Random Sampling
d) Simple Random Sampling
2) A cancer researcher performs a hypothesis test to determine the effectiveness of a new
treatment. Her test results in a p-value graters than her chosen significant level of = 0.01. The
researcher should:
a) reject the null hypothesis, because the data supports the alternative hypothesis
b) accept the null hypothesis, because the data supports the null hypothesis
c) fail to reject the null hypothesis, because the data does not support the alternative hypothesis
d) accept the alternative hypothesis, because the data does not support the null hypothesis
MATH 1040 Final Exam – Page 2
3) Past data indicates that the employed portion of the US population is 58.5% (for people 16 years
of age or older). If you wanted a margin of error of no more than 2%, how big a sample size would
you need to find a 95% confidence interval estimate for , the true current employed
percentage?
a) 2332
b) 2518
c) 2275
d) 2198
4) A study is tracking the number of airline passengers that go through special screening procedures
each hour. Which of the following would be an appropriate classification of this measured
variable?
a) Interval & Continuous
b) Ratio & Discrete
c) Interval & Discrete
d) Ratio & Continuous
5) Professor Campbell recorded scores for an exam in his Introductory Statistics course. He finds that
the mode is 77, the median is 79, and the mean is 85. When he creates a histogram of this data,
the graph will most likely appear:
a) Uniformly distributed
b) Normally distributed
c) Right-Skewed
d) Left-Skewed
6) Past data suggests that only 18% of registered voters participate in primary elections. If one were
to take a simple random sample of 30 registered voters, which most closely approximates the
probability that exactly 5 of them will participate in primary elections?
a) 16.7%
b) 35.1%
c) 23.7%
d) 18.9%
MATH 1040 Final Exam – Page 3
7) Lifespan for Kenyan bull elephants (assuming they die of natural causes) is roughly normally
distributed with a mean of 58 years and a standard deviation of 6 years. Using the Empirical Rule,
approximately what percent of elephants live between 52 and 70 years?
a) 81.5%
b) 95%
c) 77.5%
d) 68%
8) Data is drawn from a population known to be approximately normally distributed (as indicated by
historical data). If a sample of 9 observations has a sample mean of 335 and a sample standard
deviation of 80, which of the following would be a 90% confidence interval for the population
mean?
a) (282.7, 387.3)
b) (285.4, 384.6)
c) (291.1, 378.9)
d) (296.3, 373.7)
9) Which of the following is necessarily true of the sampling distribution for a sample proportion?
a) The distribution will be normally distributed for any sample size
b) The standard deviation of the sampling distribution will shrink as sample size increases
c) The point estimate, , will be equal to the population proportion, , if a large sample is used
d) The mean of the sampling distribution will grow as sample size increases
MATH 1040 Final Exam – Page 4
PART II – Each problem in this section is worth 10 points, but may be separated into multiple parts,
with point distribution indicated in each part. Partial credit may be awarded, so it is highly
recommended that you show supporting work.
10) The frequency table below lists results from a survey of Chicago sports fans; survey questions
included age and favorite team to watch:
AGETEAM Da Bears Da Bulls Da Cubs Total
18-29 371 528 193 1092
30-49 482 349 290 1121
50-69 235 177 626 1038
Total 1088 1054 1109 3251
a) If one of the fans from the survey were to be randomly selected, find the probability that this
person is either under 30 years old or prefers Da Bulls. (5 pts)
b) Find the probability that a randomly selected fan prefers Da Cubs, given that their age is
between 50 and 69. (5 pts)
11) A professor is throwing a party with raffle door-prizes and expects that 20 people will attend;
suppose no person can win multiple prizes.
a) If the three prizes are each $20, how many different ways can the winners be picked? (5 pts)
b) If the three prizes are $10, $20, and $30, how many different ways can the winners be picked?
(5 pts)
MATH 1040 Final Exam – Page 5
12) The Nielsen Company has electronically recorded data for number of hours of TV watched per
month in 24 randomly selected households in Salt Lake County:
16 26 33 38 41 43 43 46 47 54 55 58
60 61 61 64 65 72 79 92 98 113 125 140
a) Make a stemplot for this data. (4 pts)
b) What is the most appropriate measure of center for this data? (2 pts)
c) Find the 5-Number Summary for this data. (4 pts)
13) Data indicates that ACT scores are normally distributed with a population mean value of 21 and a
population standard deviation of 4.
a) What percent of scores are greater than or equal to 24? (5 pts)
b) What score marks the 35th percentile? (5 pts)
MATH 1040 Final Exam – Page 6
14) The Soylent Corporation hopes to show increase in production over recent years. In the past,
Soylent produced an average of 60 tons of food every day. A recent random sample of 36 days
shows a sample average of 63 tons per day, with a standard deviation of 5 tons. Assume the daily
yield is normally distributed.
a) State the null and alternative hypotheses to test the claim that average production has
increased. (2 pts)
b) Calculate the test statistic. (2 pts)
c) Determine the critical value or the p-value for the test statistic. (2 pts)
d) Determine whether or not to reject the null hypothesis if = 0.10. Justify your decision with
statistical reasoning. (2 pts)
e) Based on your results, does the Soylent Corporation have statistically significant evidence to
support their claim that the average production has increased? Why or why not? (2 pts)
MATH 1040 Final Exam – Page 7
15) Researchers at Utah State University conducted a study of families with children, in which the
measured variables are age at time of first marriage ( ) and years waited after marriage until
first child is born ( ) (Note that can take negative values). The study selected a random sample
of 28 families with children from Weber County. Examining the scatterplot showed that the data
follow an approximately linear pattern with no outliers. Sample summary statistics include a
mean of 28 and a standard deviation of 3.4 for age, a mean of 4 and a standard deviation of 1.7
for years waited, and a correlation coefficient of −0.66. For this sample size, this linear
correlation is statistically significant.
Recall that, for a Least-Squares Regression Line, =

and = − .
a) Write the equation for the Least-Squares Regression Line for this data. (4 pts)
b) Predict the number of years waited after marriage until the first child is born for a person who
gets married at age 36. (4 pts)
c) Explain the meaning of the slope of the regression line in the context of this study. (2 pts)
MATH 1040 Final Exam – Page 8
16) The following data represents the number of sick days taken per year by federal employees:
0 1 2 3 4 5 6 7 8
( ) 0.07 0.18 0.24 0.28 0.13 0.04 0.03 0.02 0.01
Find the expected (mean) number of sick days taken per year by federal employees. (10 pts)
17) A random sample of Allstate customers in Tooele County yields the
following data for ages ( ) and monthly auto insurance premiums ( ):
a) Calculate the correlation coefficient for the data (5 pts)
b) Determine if there is significant linear correlation between the variables based on this data.
Justify your answer statistically, using a significant level of ( = 0.05) (5 pts)

18 70
39 43
51 36
44 41
29 59
35 52
26 73
30 55
MATH 1040 Final Exam – Page 9
18) Average hit total for one team in a Major League Baseball game is 8.5 per game, with a standard
deviation of 2.6. Hits per game are normally distributed. Detroit averaged 11 hits per game in
their last 12 games, while San Francisco averaged 16 hits per game in their last 3 games.
Determine which event was a more statistically significant occurrence. (10 pts)
19) Scores in Summer Semester college courses generally have different averages than their Fall and
Spring counterparts; as well, they generally have different variability. Suppose that, for a sample
of 32 math students, their final exam scores have an average of 78.6 with a sample standard
deviation of 8.2. Find a 95% confidence interval for , the population standard deviation for
Summer Semester math final exam scores. (10 pts)
MATH 1040 Final Exam – Page 10
20) The Disney Corporation claims that the majority of the US population will flock to theaters to see
the new Star Wars movie in 2015. A simple random sample of 1138 individuals finds that 592 of
those sampled do intend to see the movie in theaters. Using this data, conduct an appropriate
hypothesis test on the Disney Corporation’s claim. Test at the = 0.02 level. (10 pts)
Statistics Formulas and Tables
Descriptive Statistics Probability

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