Download Test 1 Practice Key

Elementary Statistics
Practice Test 1
Chapters 1 and 2
Chapter 1
1. A marketing company is interested in the proportion of people who will buy a particular
product. Identify: a. the population, b. the sample, c. the parameter, d. the statistic,
e. the possible data values, and f. the data type.
Solution: a. all people (maybe in a certain geographic area, such as the United
States); b. the group of the people sampled by the marketing company; c. the
proportion of all people in the population who will buy the product; d. the proportion
of the sample who will buy the product; e. buy, not buy; f. categorical
2. Identify the data type: quantitative discrete, quantitative continuous, or categorical.
(a) number of students enrolled at a college
(b) brand of toothpaste
(c) percent of body fat
Solution: a. quantitative discrete; b. categorical; c. quantitative continuous (this
calculation involves measurements)
3. A reporter collects a sample of students at a local college by randomly selecting a proportional number of students from each major, including “undecided”. Identify the
sampling method.
Solution: stratefied sampling (the research may need to take care with students
with double-majors, since they have a higher chance of being selected)
4. Crime-related and demographic statistics for 47 US states in 1960 were collected from
government agencies, including the FBI’s Uniform Crime Report. One analysis of this
data found a strong connection between education and crime indicating that higher levels
of education in a community correspond to higher crime rates.
Which of the potential problems with samples discussed in Section 1.2 could explain this
connection?
Elementary Statistics
Practice Test 1 - Page 2
Chapters 1 and 2
Solution: Correlation versus causality: The fact that two variables are related does
not guarantee that one variable is influencing the other. We cannot assume that crime
rate impacts education level or that education level impacts crime rate. Confounding:
There are many factors that define a community other than education level and crime
rate. Communities with high crime rates and high education levels may have other
lurking variables that distinguish them from communities with lower crime rates
and lower education levels. Because we cannot isolate these variables of interest, we
cannot draw valid conclusions about the connection between education and crime.
Possible lurking variables include police expenditures, unemployment levels, region,
average age, and size.
5. Sixty adults with gum disease were asked the number of times per week they used to
floss before their diagnosis. The (incomplete) results are shown below.
Number of flosses per week
0
1
3
6
7
Frequency
27
18
Relative Frequency
0.45
Cumulative Relative Frequency
0.933
3
1
0.05
0.017
(a) Complete the table.
(b) What percent of adults flossed at least six times per week?
(c) What percent of adults flossed at most three times per week?
Solution:
Flosses per wk Freq.
0
27
1
18
a.
3
11
6
3
7
1
Rel. Freq.
0.45
0.3
0.183
0.05
0.017
Cum. Rel. Freq.
0.45
0.75
0.933
0.983
1
b. 6.7%; c. 93.3%
6. How does sleep deprivation affect your ability to drive? A recent study measured the
effects on 19 professional drivers. Each driver participated in two experimental sessions:
one after normal sleep and one after 27 hours of total sleep deprivation. The treatments
were assigned in random order. In each session, performance was measured on a variety
of tasks including a driving simulation.
Identify explanatory and response variables, treatments, experimental units, and the
control (placebo) group.
Elementary Statistics
Practice Test 1 - Page 3
Chapters 1 and 2
Solution: Explanatory variable: amount of sleep
Response variable: performance measured in assigned tasks
Treatments: normal sleep and 27 hours of total sleep deprivation
Experimental Units: 19 professional drivers
Control/Placebo: completing the experimental session under normal sleep conditions
7. The graph in below shows the number of complaints for six different airlines as reported
to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran
Airlines have far fewer complaints reported than American, Delta, and United. Can we
conclude that American, Delta, and United are the worst airline carriers since they have
the most complaints?
Solution: You cannot assume that the numbers of complaints reflect the quality of
the airlines. The airlines shown with the greatest number of complaints are the ones
with the most passengers. You must consider the appropriateness of methods for
presenting data; in this case displaying totals is misleading.
Chapter 2
8. Create a stemplot for the miles per gallon rating for 30 cars as shown below (lowest to
highest). 19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36,
37, 37, 38, 38, 38, 38, 41, 43, 43.
Stem
1
2
Solution:
3
4
Leaf
999
0115556689
11223456778888
133
Elementary Statistics
Practice Test 1 - Page 4
Chapters 1 and 2
9. Examine the overlay of relative frequency polygons in Example 2.11 (Figure 2.9). The
Final Test Grades are represented by the dark blue line. The Final Grades are represented by the light blue line.
a. Judging by the frequency polygons, which do you think is greater: the mean of the
final test grades or the mean of the final grades?
b. Use class midpoints and the frequencies in Table 2.16 to estimate the mean of the
final test grades.
c. Use class midpoints and the frequencies in Table 2.17 to estimate the mean of the
final grades.
d. Do your estimates agree with your conclusion in part (a)?
e. Why are the means found in parts (b) and (c) estimates and not exact mean scores?
Solution:
a. It appears that the final test grades have a higher mean. At the upper end,
there is a class (centered at 94.5) that has than 10 more test grades than final
grades. At the lower end, there is a class (centered at 54.5) that has 5 more
final grades than test grades.
b. 79.5 (Use the midpoints of each class as the “x” value, then find the mean of
the frequency table as usual.)
c. 77
d. Yes
e. We don’t have the actual list of test grades, so we can’t find the exact mean.
We are using the midpoint of each class to approximate every grade that falls
in that class. For example, we are using 74.5 to approximate all 30 final test
grades between 69.5 and 79.5, whereas the actual grades are most likely not all
74.5.
10. We are interested in the number of years students in a particular elementary statistics
class have lived in California. The information in the following table is from the entire
class.
Number of years Freq. Number of Years Freq.
7
1
22
1
14
3
23
1
15
1
26
1
18
1
40
2
19
4
42
2
20
3
Total = 20
Elementary Statistics
Practice Test 1 - Page 5
Chapters 1 and 2
a. List the data values sorted smallest to largest.
b. Use the data to make a boxplot on your calculator. List the 5 number summary,
the 5 values marked on the boxplot, using appropriate symbols.
c. 75% of students in this class have lived in California longer than
years.
d. Find and interpret P80 .
e. Find and interpret the percentile of 20 years.
f. Is this population or sample data?
g. Find the mean and standard deviation of the data. Use the appropriate symbols
and units.
h. Find the z scores of 7 years and 26 years. Use two decimal places. Which is more
unusual relative to the rest of the class?
i. Find the number of years living in California that is two standard deviations below
the mean.
j. Make a modified boxplot of the data on your calculator. (This is the fourth graphing
option; it looks like a boxplot, but has extra dots. These dots represent what the
calculator decides are outliers.)
(a) Which data values does the calculator list as outliers? (Use “TRACE”.)
(b) Does the formula the book suggests for identifying outliers (using the IQR)
agree with this choice of outliers? (Show your work.)
k. Which measure of center is the most representative of this data, the mean or the
median? Explain.
Solution:
a. 7, 14, 14, 14, 15, 18, 19, 19, 19, 19, 20, 20, 20, 22, 23, 26, 40, 40, 42, 42
b. min = 7, Q1 = 16.5, med = 19.5, Q3 = 24.5, max = 42
c. 16.5
d. P80 = 33 years. 80% of students in this class have lived in California shorter
than 33 years. 20% of students in this class have lived in California longer than
33 years.
e. 20 years marks the 58th percentile, or P58 = 20 years. 58% of students in this
class have lived in California less than 20 years; 42% for longer than 20 years.
f. This is population data. (The description says that we are interested in this
particular class only, and this is all the data from this class.)
Elementary Statistics
Practice Test 1 - Page 6
Chapters 1 and 2
g. µ = 22.7years, σ = 10.0years. (Note that we are using the population parameter symbols and the population formula for standard deviation from the
calculator. Round to one decimal place, since the data has zero decimal places.)
h. 7 years: z = −1.57. 26 years: z = 0.34. 7 years is more unusual relative to the
rest of the class because it is more standard deviations from the class mean.
(Remember not to round until the end of the calculation.)
i. 2.7 years is 2 standard deviations below the mean.
j. (a) 40, 42
(b) Yes. According to the formula, low outliers are below 16.5 − 1.5(8) = 4.5
years and high outlliers are above 24.5 + 1.5(8) = 36.5 years.
k. The median is the best representative of the bulk of the data because the
outliers skew the mean to the right, making it appear that the students have
lived in California longer than they actually have. Only 6 students have lived
in California longer than the mean of 22.7 years.
Many of these problems are from Barbara Illowsky & Susan Dean. “Introductory Statistics.” OpenStax College, 2013. iBooks.
(Chapters 1 and 2) https://itun.es/us/kFeL1.l