Practice Test Questions

Question 1

If a numerical measure describes an aspect of a sample, is it a statistic or a parameter?

Answer 1

Statistic

Question 2

If a variable describes an individual by placing the individual in a category or group, is the variable quantitative or qualitative?

Answer 2

Qualitative

Question 3

If data consist of names, labels, or categories with no implied criteria by which the data can be ordered from smallest to largest. What is the highest level Of measurement for the data: nominal, ordinal, interval. or ratio?

Answer 3

Nominal (Trick question since data can be ordered, but isn’t)

Question 4

If it makes sense to say that one data measurement in a data set is twice that of another measurement in the set. what is the highest level of measurement for the data: nominal, ordinal, interval, or ratio?

Answer 4

Ratio (Anything scaled by a multiple = Ratio)

Question 5

Consider a sample of size n. If every sample of size n has equal chance of selected, what is the type of sample: stratified, systematic. simple random, cluster?

Answer 5

Simple Random

Question 6

If a treatment is applied to subjects or objects in a study in order to observe a possible change in the variable of interest. Is the study an observational study or an experiment?

Answer 6

Experiment

Question 7

Sudoku is a puzzle consisting of squares arranged in 9 rows and 9 columns. fie 81 squares are further divided into nine 3 x 3 square boxes. The object is to fill in the squares with numerals 1 through 9 so that each column, row, and box contains all nine. However, there is a requirement that each number appear only once in any row, column, or box. Each puzzle already has numbers in some of the squares. Would it appropriate to use a random-number table to select a digit for each blank square?

Answer 7

Because of the requirement that each appear number only once in a given column, row, or box, it would be very inefficient to use a random-number table to select the numbers. It’s better to simply look at existing numbers. list possibilities that meet the requirement, and eliminate numbers that don’t work.

Question 8

Alisha wants to do a statistical study to determine how long it takes people to complete a Sudoku puzzle: Her plan is as follows: 1. Download 10 different puzzles from the Internet. 2. Find 10 friends willing to participate. 3. Ask each friend to complete one of the puzzles and time him or herself. 4. Gather the completion times from each friend. Describe some of the problems With Alisha’s plan for the study. Are the results from Alisha’s study anecdotal. or do they apply to the general population?

Answer 8

There are many problems. For instance, it is not clear that the puzzles she wants to download are of the same difficulty. Friends willing to participate may have different levels of experience with the puzzles. Conditions under which the puzzles are solved are not specified. The results of the study would be case by case, therefore anecdotal.

Question 9

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: A. How many hours are you scheduled to work each week? Answer to the nearest hour. B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (a) Suppose you take random samples from the following groups: freshman. sophomores, juniors, and seniors. What kind of sampling techniques are +you using (simple random, stratified, systematic, cluster, multistage, convenience)?

Answer 9

Stratified

Question 10

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: A. How many hours are you scheduled to work eachweek? Answer to the nearest hour. B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (b) Who are the individuals in the study?

Answer 10

Students on your campus with work-study jobs

Question 11

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: A. How many hours are you scheduled to work each week? Answer to the nearest hour. (c) What is the variable for question A? Classify the variable as qualitative or quantitative. What is the level of the measurement?

Answer 11

Hours scheduled; quantitative; ratio.

Question 12

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (d) What is the variable for question B? Classify the variable as qualitative or quantitative. What is the level of the measurement?

Answer 12

Rating of applicability of work experience to future employment; qualitative; ordinal.

Question 13

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (e) Is the proportion of responses “3 = very” to question B a statistic or a parameter?

Answer 13

Statistic (Trick question, 3 = Very is a Parameter but the Proportion of answers is a Statistic)

Question 14

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: A. How many hours are you scheduled to work each week? Answer to the nearest hour. B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (f) Suppose only of the students you selected for the sample respond. What is the nonresponse rate? Do you think the nonresponse rate might introduce bias into the study? Explain.

Answer 14

60%; the people choosing not to respond may have some characteristics, such as not working many hours, that would bias the study

Question 15

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are: A. How many hours are you scheduled to work each week? Answer to the nearest hour. B. How applicable is this work experience to your future employment goals? Respond using the following scale: I = not at all, 2 = somewhat, 3 = very. (g) Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.

Answer 15

No. The sample frame is restricted to one campus.

Question 16

A radio talk show host asked listeners to respond either yes or no to the question, “Is the candidate who spends the most on a campaign the most likely to win?” Fifteen people called in, and nine said yes. What is the implied population?

Answer 16

Population: opinions of all listeners

Question 17

A radio talk show host asked listeners to respond either yes or no to the question, “Is the candidate who spends the most on a campaign the most likely to win?” Fifteen people called in, and nine said yes. What is the variable?

Answer 17

variable: opinion of a caller

Question 18

A radio talk show host asked listeners to respond either yes or no to the question, “Is the candidate who spends the most on a campaign the most likely to win?” Fifteen people called in, and nine said yes. Can you detect any bias in the selection of the sample?

Answer 18

Yes. a voluntary response

Question 19

The U.S. Department of Justice examined all reported cases of identity theft for U.S. residents aged 16 or older. Their data show that of all the reported incidents of identity theft in a recent year. 40% involved existing credit card accounts. You are to design a simulation of seven reported identity thefts showing which ones involve existing credit card accounts and which ones do not. How would you assign the random digits 0 through 9 to the two categories “Does” and “Does not” involve existing credit card accounts? Use your random-digit assignment and the random-number table to generate the results from a random sample of seven identity thefts. If you do the simulation again, do you expect to get exactly the same results?

Answer 19

Assign the digits so that 4 out of the 10 digits (0 through 9) correspond to the result “Does” and 6 of the digits correspond to the result “Does not” involve existing credit card accounts. One assignment is digits 1, 2, 3 correspond to “Does” while the remaining digits 4, 5, 6. 7, 8, 9 correspond to “Does not” involve such accounts. Starting with line 1, block 1 of Table 1, the sequence gives “Does not,” “Does,” “Does not,” “Does,” “Does.” “Does not.” “Does not.” We cannot necessarily expect another simulation to give the same result. The results depend on the response assigned to the digits and the section of the random. number table used.

Question 20

What type of sampling is used in the following? (simple random, stratified, systematic, cluster, or convenience) To conduct a pre-election opinion poll on a proposed amendment to the state constitution. a random sample of 10 telephone prefixes (first three digits of the phone number) was selected, and all households from the phone prefixes selected were called.

Answer 20

Cluster

Question 21

What type of sampling is used in the following? (simple random, stratified, systematic, cluster, or convenience) To conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used.

Answer 21

Convenience

Question 22

What type of sampling is used in the following? (simple random, stratified, systematic, cluster, or convenience) To maintain quality control in a brewery, every 20th bottle of beer coming off the production line was opened and tested.

Answer 22

Systematic

Question 23

What type of sampling is used in the following? (simple random, stratified, systematic, cluster, or convenience) Subscribers to a new smartphone app that streams songs were assigned numbers. Then a sample of 30 subscribers was selected by using a random-number table. The subscribers in the sample were invited to rate the process for selecting the songs in playlist.

Answer 23

Random

Question 24

What type of sampling is used in the following? (simple random, stratified, systematic, cluster, or convenience) To judge the appeal of a proposed television sitcom, a random sample of to people from each of three different age categories was selected and those chosen were asked to rate a pilot show.

Answer 24

Stratified

Question 25

What type of graphing is used in the following? (histogram, relative frequency graph, ogive) Shows cumulative frequency (or percent of data) falling at or below each upper class boundary in a frequency table

Answer 25

Ogive

Question 26

What type of graphing is used in the following? (histogram, relative frequency graph, ogive) Shows number of data falling within each distinct class of a frequency table.

Answer 26

Histogram

Question 27

What type of graphing is used in the following? (histogram, relative frequency graph, ogive) Shows the relative frequency (or percent) or all data falling within each class of a frequency table

Answer 27

relative frequency

Question 28

Which type(s) of data can be shown in a histogram? (quantitative, qualitative (also known as category). or both)

Answer 28

quantitative

Question 29

Which type(s) of data can be shown in a bar graph? (quantitative, qualitative (also known as category). or both)

Answer 29

Both

Question 30

Which graphical display shows each data value (or truncated data value) in order from smallest to largest: histogram, pie chart, or stem-and-leaf?

Answer 30

Steam and Leaf

Question 31

If a histogram is skewed left, more or the data falls on which side? right or left?

Answer 31

Right

Question 32

How are data plotted in a time-series graph: by in order from smallest to largest, or at regular intervals over time

Answer 32

at regular intervals over time

Question 33

Consider these types of graphs: histogram, bar graph, Pareto chart, pie chart, stem-and-leaf display. (a) Which are suitable for qualitative data? (b) Which are suitable for quantitative data?

Answer 33

(a) Bar graph, Pareto chart, pie chart. (b) All.

Question 34

A consumer interest group is tracking the percentage of household income spent on gasoline over the past years. Which graphical display would be more useful, a histogram or a time-series graph? Why?

Answer 34

Time series

Question 35

Describe how data outliers might be revealed in histograms and stem-and-leaf plots.

Answer 35

Any large gaps between bars or stems with leaves at the beginning or end of the data set might indicate that the extreme data values are outliers.

Question 36

How are dotplots and stem-and-leaf displays similar? how are they different?

Answer 36

Dotplots and stem-and-leaf displays both show all the data values. Stem-and-leaf displays group all data values having the same stem, whereas dotplots group only data values that are exactly the same.

Question 37

The timeplot gives the number of state and federal prisoners per 100,000 population
(a) Estimate the number of prisoners per people for 1980 and for 1997.

Answer 37

140 in 1980 and 440 in 1997

Question 38

The timeplot gives the number of state and federal prisoners per 100,000 population

b) During the period shown. there was increased prosecution of the offenses, longer sentences for conunnn crimes, and reduced access to parole. What does the time-series graph say about the prison population change per 100,000 people?

Answer 38

It is Increasing

Question 39

The timeplot gives the number of state and federal prisoners per 100,000 population

(c) In 1997, the U.S. population was approximately 266,574,000 people. At the rate of 444 prisoners per 100,000 population, about how many prisoners were in the system?

The projected U.S. population for the year 2020 is 323,724,000.

If the rate of prisoners per 100,000 stays the same as in
1997, about how many prisoners do you expect will be in the system in 2020?

Answer 39

1,183.589; 1437.335.

Question 40

Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol. This distribution is based on the age distribution of DUI arrests given in the Statistical Abstract of rhe United States (12th edition).

(b) Is it skewed to the right or left?

Answer 40

Slightly right

Question 41

Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol. This distribution is based on the age distribution of DUI arrests given in the Statistical Abstract of rhe United States (12th edition).

(b) Make a frequency table with seven classes showing class limits, class boundaries, midpoints, frequencies, and relative frequencies.

Answer 41

Question 43

Consider the following measures of central tendency: mean.
median, mode. Match each type to the appropriate description:
(i) the central value o fa data set after it has been ordered from smallest to largest
(ii) the data value occurring most frequently in a data set
(iii) the sum of all the data values in a data set divided by the number of data values in the set

Answer 43

(i) Median. (ii) Mode. (iii) Mean

Question 44

Consider the statement: For a trimmed mean, we eliminate the bottom 5% of the data from an ordered data set and then compute the mean of the remaining data. Is the statement true or false?

Answer 44

False: Eliminate 5% of the data from both the bottom and the top Of the ordered

Question 45

When we compute a sample standard deviation of a data set
Terminology do we subtract the sample mean or the sample median from each of the data

Answer 45

Sample Mean

Question 46

Consider the following terms: outlier, coefficient of variation,
range. Match each term to the appropriate description.
(i) The difference between the largest and the smallest data value of a data set
(ii) The spread of a data set measured by the standard deviation relative 10 the
mean of the data set
iii) An unusually targe or small data value in a data set

Answer 46

(i) Range (ii) Coefficient of variation (iii) Outlier

Question 47

Terminology
Consider the following symbols: s,σ,x̅,μ

Match each of the symbols to the appropriate name:

(i) sample mean (ii) sample standard deviation
(ii) population mean (iv) population standard deviation

Answer 47

• *1. x̅
  2. s
  3. μ
  4. σ**

Question 48

How is the standard deviaion related to the variance of a data set

Answer 48

The standard deviation is the square root of the variance.

Question 49

In a box-and-whisker plot, which measure of central tendency is displayed: mean, median, or mode?

Answer 49

Median

Question 50

Consider the following statement: If you answered 90% of the
questions on a test correctly, then your score is in the 90th percentile, T/F? Explain.

Answer 50

False. The 90th percentile refers to a score 90% of the scores fall at or below.

Question 51

What measures of variation indicate spread about the mean?

Answer 51

Variance and standard deviation,

Question 52

Which graphic display shows the median and the data spread about the median?

Answer 52

Box and Whisker Plot

Question 53

Look at the two histograms, each involves the same number of data. The data are the whole numbers, so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis. Notice both are symmetric.

(b) Which distribution has the larger standard deviation? Why?

Answer 53

The second one since more of the data are farther away from the mean.

Question 54

Look at the two histograms, each involves the same number of data. The data are the whole numbers, so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis. Notice both are symmetric.

a) Estimate the mode, median, and mean for each histogram.

Answer 54

For both histograms, mode = 7; median = 7; mean = 7.

Question 55

Consider the following Minitab display of two data sets.

(c) Compare the interquartile ranges of the two sets. How do the middle halves of the data sets compare?

Answer 55

The C1 distribution has a larger interquartile range that is symmetric around the median.
The C2 distribution has a very compressed interquartile range with the median equal to Q3.

Question 56

Consider the following Minitab display of two data sets.

(b) Which data set seems more symmetric? Why?

Answer 56

The Cl distribution seems more symmetric because the mean and median are equal, and the median is in the center of the interquartile range. In the C2 distribution, the mean is less than the median.

Question 57

Consider the following Minitab display of two data sets.

(a) What are the respective means? the respective ranges?

Answer 57

For both data sets, mean = 20 and range = 24.

Question 58

“Radon: The Problem No One Wants to Face” is the title of an article appearing in Consumer Reports. Radon is a gas emitted
from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable.” Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L):

1. 9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
   (c) Based on the data, would you recommend radon mitigation in this house? Explain.

Answer 58

Yes

Question 59

“Radon: The Problem No One Wants to Face” is the title of an article appearing in Consumer Reports. Radon is a gas emitted
from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable.” Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L):

1. 9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
   (b) Find the sample standard deviation, coeffcient of variation. and range.

Answer 59

s - 2.46;
cv- 544%;
range = 6.7.

Question 60

“Radon: The Problem No One Wants to Face” is the title of an article appearing in Consumer Reports. Radon is a gas emitted
from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable.” Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L):

1. 9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
   (a) Find the mean, median, and mode.

Answer 60

mean = 4.53;
median = 4.05
mode = 1.9

Question 61

31 33 34 34 35 35 35 36 38 38 38 39 40 40 40 40
41 41 41 41 41 41 41 42 42 43 44 44 44 45 45 46
46 46 46 47 48 49 49 49 49 50 51 52 52 53 53 53
53 53 55 56 56 57 57 59 62 66 66 68

(b) Get Sample Mean and Sample Standard Deviation

Answer 61

Mean = 46.15
s = 8.63

Question 62

31 33 34 34 35 35 35 36 38 38 38 39 40 40 40 40
41 41 41 41 41 41 41 42 42 43 44 44 44 45 45 46
46 46 46 47 48 49 49 49 49 50 51 52 52 53 53 53
53 53 55 56 56 57 57 59 62 66 66 68

(b) Make a frequency table using five classes. Then estimate the meanand sample standard deviation using the frequency table.
Compute a 75% Chebyshev interval centered around the mean.

Answer 62

Question 63

31 33 34 34 35 35 35 36 38 38 38 39 40 40 40 40
41 41 41 41 41 41 41 42 42 43 44 44 44 45 45 46
46 46 46 47 48 49 49 49 49 50 51 52 52 53 53 53
53 53 55 56 56 57 57 59 62 66 66 68

(a) Make a box-and-whisker plot of the data. Find the interquartile range.

Answer 63

Low = 31;
Q1 = 40;
median = 45; 
Q3 = 52.5:
high = 68;
IQR = Q3 - Q1 = 12.5.