Download Review for Elementary Statistics Exam 1 Dr. Schultz 1. Consider the

Review for Elementary Statistics Exam 1
Dr. Schultz
1.
Consider the following heart rates (in beats per minute) of a sample of bus drivers:
74 53 60 84 52 76 68 63
67 54 64 73 63 73 66 59
77 54 71 68 57 60 66 64
80 77 55 82 77 63 71 89
a. Construct a stem-and-leaf plot of this data.
b. Construct an expanded stem-and-leaf plot of this data.
2.
Student scores on the SAT are reported on a scale that ranges from a low of 200 to a high of 800. In one high
school graduating class, the mean math SAT score was 493 with a standard deviation of 105, and the mean verbal
SAT score was 420 with a standard deviation of 98. One student from this graduating class had a 703 math score
and a 665 verbal score. Relative to the other students in her graduating class, on which section of the SAT did this
student do better? Explain your answer.
3.
When Abe Lincoln was first elected president, he received 39.82% of the 1,865,908 votes cast.
a. Is “39.82%” a statistic or a parameter?
b. Compute the number of votes that Abe Lincoln received. Is this value from a discrete or a continuous
data set?
c. Which level of measurement was used (nominal, ordinal, interval, or ratio)?
4.
Consider the following weights (in pounds) obtained from a sample of 18-24-year-old males:
129.2 185.3 218.1 182.5 142.8
155.2 170.0 151.3 187.5 145.6
167.3 161.0 178.7 165.0 172.5
191.1 150.7 187.0 173.7 178.2
161.7 170.1 165.8 214.6 136.7
278.8 175.6 188.7 132.1 158.5
146.4 209.1 175.4 182.0 173.6
149.9 158.6
a. Construct a frequency distribution for this data set. Use a class width of 20 and a lower class limit of
120.0 for your first class.
b. What are the class midpoints?
c. What are the upper class limits?
d. What are the class boundaries?
e. Use your frequency distribution to plot a histogram.
f. Construct a relative frequency distribution for this data set.
g. Construct a cumulative frequency distribution for this data set.
5.
Botany students recorded the following sample of tree circumferences (in feet):
1.8 1.9 2.4 5.1 3.1 5.5 5.1 8.3 13.7 5.3
4.9 3.7 3.8 4.0 3.4 5.2 4.1 3.7 3.9
1.8
a. Is the population these data values are drawn from discrete or continuous?
b. What level of measurement was used (nominal, ordinal, interval, or ratio)?
c. Find the standard deviation.
d. Find the five-number summary and use it to construct a boxplot.
e. Are there any outliers? If so, then construct a modified boxplot.
f. Find P10.
g. Find P36.
h. What tree circumference corresponds to the 83rd percentile?
i. What percentile is a tree circumference of 13.7 feet?
j. Convert the circumference of 13.7 feet to a z score.
k. In the context of this data set, is a circumference of 13.7 feet unusual? Why or why not?
l. Use the range rule of thumb to identify any other unusual circumference values in this data set.
m. Construct a frequency distribution. Use 7 classes with 1.0 as the lower limit of the first class, and use a
class width of 2.0.
2
6.
Consider the following frequency distribution of the ages of U.S. presidents when they were inaugurated:
Age
Frequency
40 - 44
2
45 - 49
6
50 - 54
13
55 - 59
12
60 - 64
7
65 - 69
3
a.
b.
What is the mean of the original data set?
What is the standard deviation of the original data set?
7.
Find the probability of Lucky Lu winning her next race if the actual odds against her winning are 32:1.
8.
Adults are randomly selected for a Gallup Poll and asked if they think that human cloning should be allowed.
Among the adults surveyed, 91 said it should be allowed, 901 said it should not be allowed, and 20 had no
opinion. Estimate the probability that a randomly selected adult believes that human cloning should be allowed.
9.
A balanced quarter is tossed 4 times.
a. Construct the sample space
b. Find the probability that exactly three of the four tosses will come up heads.
c. Find the probability that the second toss comes up tails.
d. Find the probability that all four tosses come up the same.
e. Find the probability that the last two tosses will come up heads.
10. Consider the following results of a test for marijuana use among job applicants:
Actually used marijuana Did not actually use marijuana
Positive test result
119
24
(Marijuana is present)
Negative test result
3
154
(Marijuana is absent)
a. Find the probability of a wrong test result for a person who does not use marijuana. Is it “unusual” for
the test result to be wrong for those not using marijuana?
b. Find the probability of a wrong test result for a person who does use marijuana. Is it “unusual” for the
test result to be wrong for those not using marijuana?
11. The card game of solitaire was played 500 times so that the probability of winning could be estimated. Among the
500 trials, the game was won 77 times. Based on these results, find the odds against winning.