Deck 12: Statistical Reasoning

Question 1

Suppose a quality control inspector pulls every tenth can of soup from a conveyor belt to ensure that the cans are filled to capacity. How should this procedure be evaluated?

A) The sample may not be a random sample.
B) The procedure is defective because it fails to specify which can is selected first.
C) The procedure guarantees that the sample is a random sample.
D) The sample is not large enough for the kind of test being done.
E) The procedure calls for an excessively large sample.

Answer 1

The sample may not be a random sample.

Question 2

Suppose that two sets of data conform to a normal probability distribution, and that the standard deviation of Set X is 2, while the standard deviation of Set Y is 3. Then,

A) Set X contains a larger amount of data than set Y.
B) The curve for Set Y is more flattened and spread out than the curve for Set X.
C) The variance for both sets of data will be the same.
D) The curve for Set X is more flattened and spread out than the curve for Set Y.
E) Set Y contains a larger amount of data than set X.

Answer 2

The curve for Set Y is more flattened and spread out than the curve for Set X.

Question 3

Data Set 2C
Suppose that the lengths of employment (in years) of 7 employees of a small company are as follows:
1, 2, 2, 3, 4, 4, 5
What is the approximate variance for Data Set 2C?

A) 1.5
B) 1.7
C) 2
D) 1.6
E) 1.8

Answer 3

1.7

Question 4

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood:
$\begin{array} { l | l } \text { Number of } & \\\text { Houses } & \text { Age } \\\hline 2 & 1 \\5 & 3 \\1 & 4 \\3 & 6 \\4 & 9\end{array}$

-Given Data Set 1C, what is the median age of the houses?

A) 3 years.
B) 5.4 years.
C) 5 years.
D) 4 years.
E) 4.6 years.

Question 5

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood:
$\begin{array} { l | l } \text { Number of } & \\\text { Houses } & \text { Age } \\\hline 2 & 1 \\5 & 3 \\1 & 4 \\3 & 6 \\4 & 9\end{array}$

-Given Data Set 1C, what is the mean age of the houses?

A) 3 years.
B) 4.6 years.
C) 5 years.
D) 4 years.
E) 5.7 years.

Question 6

One of the problems with the Literary Digest poll taken prior to the 1936 presidential election was:

A) Many of the people in the population could not afford a telephone.
B) The sample size was too small.
C) The population was too large.
D) The responses were biased because of the way the questions were phrased.
E) Most people were not at home at the time the calls were made.

Question 7

Suppose that the average price of a piece of jewelry at Henry's Jewelers is $200, and Mr. Smith wants to spend approximately that much for his wife's birthday gift. Under what circumstances can Mr. Smith be reasonably assured of a selection of jewelry in his price range?

A) The average is a mean.
B) The jeweler has a reputation for selling quality merchandise.
C) The average is a modal average.
D) The average is a median.
E) The pieces of jewelry are reasonably priced.

Question 8

Range, variance, and standard deviation are measurements of:

A) Gradations of quality.
B) Sampling error.
C) Intensity.
D) Dispersion.
E) Quantity.

Question 9

Suppose that a poll is taken about how marriage partners relate to each other, and one of the questions asked is if the person being interviewed has ever lied to his/her spouse. Can the responses to this question be trusted?

A) Yes, because the question is very straightforward.
B) Yes, because most people are inclined to answer truthfully in a poll.
C) No, because people who have lied to their spouse would probably deny it.
D) No, because the question is ambiguous.
E) Yes, because the vast majority of marriage partners do not lie to their spouse.

Question 10

Data Set 2C
Suppose that the lengths of employment (in years) of 7 employees of a small company are as follows:
1, 2, 2, 3, 4, 4, 5
For Data Set 2C, what is the approximate standard deviation?

A) √1.8
B) 1.1
C) 1.4
D) 2
E) √1.7

Question 11

Suppose a poll is taken to sample voter preferences in an upcoming presidential election. To conduct the poll, an interviewer standing on a street corner in the financial district of a large city asks questions of people as they pass by. What result would be expected from such a poll?

A) The people on the street corner would refuse to speak to the interviewer.
B) The people interviewed would not be candid with their answers.
C) The responses would be biased in favor of the Democratic candidate.
D) The responses would be biased in favor of the Republican candidate.
E) The responses would accurately predict the outcome of the election.

Question 12

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood:
$\begin{array} { l | l } \text { Number of } & \\\text { Houses } & \text { Age } \\\hline 2 & 1 \\5 & 3 \\1 & 4 \\3 & 6 \\4 & 9\end{array}$

-Given Data Set 1C, what is the modal age of the houses?

A) 3 years.
B) 5 years.
C) 4.3 years.
D) 4 years.
E) 3.5 years.

Question 13

In a normal distribution, the data represented are:

A) Skewed away from the median point.
B) Skewed toward the mean point.
C) Random.
D) Trustworthy.
E) Shaped like a triangle.

Question 14

In general, the larger a sample is:

A) The smaller the standard deviation becomes.
B) The more likely it is that it will be biased.
C) The more difficult it becomes to avoid atypical cases.
D) The greater the standard deviation becomes.
E) The more closely it represents the population.

Question 15

Suppose that the price of crude oil, the primary raw material for gasoline, increases by 30 percent. Assuming everything else stays the same, by how much has the cost of producing gasoline increased?

A) 35 percent.
B) 32 percent.
C) 30 percent.
D) More than 35 percent.
E) Less than 30 percent.

Question 16

Suppose that a survey is taken of the adult residents of a town, and one of the questions asked is whether the person responding graduated from high school. Can the responses to this question be trusted?

A) Yes, because the question is very straightforward.
B) No, because the number of 'yes' answers would probably be skewed upward.
C) Yes, because the respondents are adults.
D) No, because the number of 'yes' answers would probably be skewed downward.
E) No, because most of the respondents would refuse to answer this question.

Question 17

Suppose that a biologist took water samples at random intervals from a rapidly flowing creek to test for contaminants. A sample was taken at a single location from the center of the creek for one year. Could such a survey be depended on?

A) Yes, because contaminants in the creek would not change from day to day.
B) No, because all the samples were taken from the center of the creek.
C) No, because a sample must be taken every day.
D) Probably.
E) No, because all the samples were taken from a single location.

Question 18

One way of exaggerating the apparent message conveyed by a bar graph is by:

A) Altering the vertical scale while leaving the horizontal scale as is.
B) Altering both the horizontal scale and the vertical scale by the same amount.
C) Altering the horizontal scale while leaving the vertical scale as is.
D) Narrowing the width of the bars.
E) Printing the bars in different colors.

Question 19

Suppose two simultaneous random surveys were taken of a mid sized city to determine public acceptance of a proposed ballot measure. Survey X covered 1000 voters, and Survey Y covered 2000 voters. How would you expect the surveys to compare for accuracy?

A) There is no way of knowing how the two surveys compare.
B) The two surveys are equally accurate.
C) Survey Y is 4 times more accurate than Survey X.
D) Survey Y is twice as accurate as Survey X
E) Survey Y is probably about one percentage point more accurate than Survey X.

Question 20

A sample that is not representative of the population from which it is drawn is said to be:

A) Compromised.
B) Distorted.
C) Biased.
D) Contaminated.
E) Unresponsive.

Question 21

In regard to the outcome of a poll, as the confidence level increases,

A) The more difficult it becomes to avoid atypical cases.
B) The standard deviation becomes smaller.
C) The margin of error increases.
D) The standard deviation becomes greater.
E) The margin of error decreases.

Question 22

Suppose a poll is taken to determine voter attitude about increasing the state income tax in exchange for increased social services (including welfare). If the poll is confined primarily to the poorer neighborhoods of the state, what results can be expected?

A) The poll would be biased against an increase in the state income tax.
B) The people interviewed would not be candid with their answers.
C) The people would refuse to speak to the interviewer.
D) The poll would be biased in favor of increased social services.
E) The responses would accurately reflect the opinion of the state's population.

Question 23

Suppose that you want to buy a pair of size 9 shoes, and you are told that the average size of the shoes in Bob's Shoe Store are size 9. Under what circumstances is this information useful to you?

A) The shoes reflect the latest fashions.
B) The standard deviation is relatively large.
C) The average is a mean.
D) The average is a modal average.
E) The average is a median.

Question 24

Data Set 2B
Suppose that the height (in meters) of 6 fir trees in the garden department of a store are as follows:
1, 2, 2, 4, 4, 5
For Data Set 2B, what is the standard deviation?

A) √2
B) 1
C) 1.3
D) 2
E) √1.5

Question 25

Suppose that the costs of operating a factory that manufactures copper pipe increase by the following amounts: copper: 6%, labor: 5%, electricity: 4%, taxes: 2%, repairs and maintenance: 3%. By how much have the costs of manufacturing the pipe increased?

A) 20%
B) 4%
C) 6%
D) Less than 2%.
E) Less than 6%.

Question 26

One way that pictograms can distort a message is by:

A) Using pastel colors to create the pictogram.
B) Using fluorescent colors to create the pictogram.
C) Blurring the lines of the pictogram.
D) Ignoring the visual effect of a three dimensional image.
E) Chopping off the bottom of the pictogram.

Question 27

If the variance of a set of data is relatively large, then:

A) The standard deviation diverges from the variance.
B) The data tend to be more spread out from the mean point.
C) The sample does not accurately represent the population.
D) The population from which the data are extracted tends to be large.
E) Most of the data fall close to the mean point.

Question 28

Suppose that the costs of operating a certain restaurant increase by the following amounts: food: 4%, labor: 5%, electricity: 3%, taxes: 2%, repairs and maintenance: 4%. By how much have the costs of operating the restaurant increased?

A) 18%
B) Less than 5%.
C) The modal average of the increases for these five items.
D) Less than 2%.
E) More than 18%.

Question 29

Data Set 1B
Suppose that the following table represents the age of the cars in a small used car lot: $$\begin{array} { l | l } \text { Number of } & \\\text { Cars } & \text { Age } \\\hline 2 & 1 \\4 & 2 \\1 & 3 \\5 & 4 \\1 & 6\end{array}$$

-Given Data Set 1B, what is the modal age of the cars?

A) 5 years.
B) 4 years.
C) 6 years.
D) 3 years.
E) 3.5 years.

Question 30

In a poll about creating a publicly funded healthcare program, suppose the question is asked, "Should free healthcare be given to people who are too lazy to work and who have never paid any taxes?" Can the answers to this question be trusted?

A) No, because the question is biased in favor of a negative answer.
B) Yes, because most people are inclined to answer truthfully in a poll.
C) Yes, because the phrasing of a question rarely affects the answer.
D) No, because the question is ambiguous.
E) Yes, if the poll is random.

Question 31

Suppose a poll shows Smith leading Jones by 52 percent to 48 percent for U.S. Senate. What can be said about the results of this poll?

A) If the margin of error is ± 1 percent, then Smith is certainly ahead of Jones.
B) If the margin of error is more than ± 2 percent, then Jones might lead Smith.
C) If the sample is random, then the results of the poll are unimpeachable.
D) If the confidence level is 99 percent, then Smith is certainly ahead of Jones.
E) If the margin of error is ± 3 percent, then Jones is ahead of Smith.

Question 32

Suppose, to select a sample from a population of 3000 persons, the following procedure is followed. The names of the people are written on identical, square pieces of thin cardboard measuring one inch on a side, and these pieces of cardboard are then tumbled in a clothes dryer (with the heat shut off). After 30 minutes, a blindfolded person reaches in and withdraws a selected number of names. What can be said about this sample?

A) The sample is probably biased because clothes dryers are not supposed to be used in collecting samples.
B) The sample is probably biased because people with shorter names would be selected first.
C) The sample is probably biased because the names on the top of the heap would be selected first.
D) The sample is probably biased because the names toward the front of the dryer would probably be selected first.
E) The sample is almost certainly random.

Question 33

One way of exaggerating fluctuations in the price of a company's stock is to:

A) Contract the horizontal scale.
B) Chop off the bottom of the graph and expand the vertical scale.
C) Chop off the top of the graph and expand the horizontal scale.
D) Use a thicker line to represent the fluctuations.
E) Alter the background color of the graph.

Question 34

If the standard deviation of a set of data is relatively small, then:

A) The sample does not accurately represent the population.
B) The standard deviation diverges from the variance.
C) The data tend to be spread out from the median point.
D) The population from which the data are extracted tends to be large.
E) Most of the data fall close to the mean point.

Question 35

Suppose that for a large population, the margin of error of Poll A is 2%, and the margin of error of Poll B is 4%. Then,

A) The sample used in Poll A is much larger than the sample used in Poll B.
B) The sample used in Poll A is slightly larger than the sample used in Poll B.
C) The sample used in Poll B is much larger than the sample used in Poll A.
D) The sample used in Poll B is slightly larger than the sample used in Poll A.
E) The difference in sampling error is unrelated to the size of the samples.

Question 36

The range of a set of data is:

A) The difference between the modal value and the mean value.
B) A measure of how much the data differ from the mean value.
C) The difference between the largest and smallest values.
D) A measure of how much the data differ from the median value.
E) The difference between the median value and the mean value.

Question 37

Suppose you are the pilot of a small commercial airplane, and you want to ensure that the plane will carry the load. What statistic would be most useful to you?

A) The mean weight of the passengers.
B) The median weight of the passengers.
C) The modal weight of the passengers.
D) The dispersion of the data representing the weight of the passengers.
E) The standard deviation of the data representing the weight of the passengers.

Question 38

Data Set 2B
Suppose that the height (in meters) of 6 fir trees in the garden department of a store are as follows:
1, 2, 2, 4, 4, 5
What is the variance for Data Set 2B?

A) √2
B) 1.5
C) 2.5
D) 1
E) 2

Question 39

Data Set 1B
Suppose that the following table represents the age of the cars in a small used car lot: $$\begin{array} { l | l } \text { Number of } & \\\text { Cars } & \text { Age } \\\hline 2 & 1 \\4 & 2 \\1 & 3 \\5 & 4 \\1 & 6\end{array}$$

-Given Data Set 1B, what is the mean age of the cars?

A) 2 years.
B) 2.5 years.
C) 3 years.
D) 4 years.
E) 3.5 years.

Question 40

Data Set 1B
Suppose that the following table represents the age of the cars in a small used car lot: $$\begin{array} { l | l } \text { Number of } & \\\text { Cars } & \text { Age } \\\hline 2 & 1 \\4 & 2 \\1 & 3 \\5 & 4 \\1 & 6\end{array}$$

-Given Data Set 1B, what is the median age of the cars?

A) 4 years.
B) 3.5 years.
C) 5 years.
D) 3 years.
E) 6 years.

Question 41

Data Set 2A
Suppose that the ages of 8 kittens in a pet shop are as follows:
1, 2, 2, 3, 3, 4, 4, 5
For Data Set 2A, what is the standard deviation?

A) √2
B) 1
C) 1.5
D) 2
E) √1.5

Question 42

Data Set 1A
Suppose that the following table represents the length of service (in years) of the employees of a business: $$\begin{array} { l | l } \text { Number of } \\\text { Employees } & \text { Years } \\\hline 1 & 1 \\6 & 2 \\1 & 3 \\3 & 4 \\4 & 5\end{array}$$

-Given Data Set 1A, what is the mean length of service of the employees?

A) 3 years.
B) 2.5 years.
C) 3.2 years.
D) 4 years.
E) 3.5 years.

Question 43

Data Set 1A
Suppose that the following table represents the length of service (in years) of the employees of a business: $$\begin{array} { l | l } \text { Number of } \\\text { Employees } & \text { Years } \\\hline 1 & 1 \\6 & 2 \\1 & 3 \\3 & 4 \\4 & 5\end{array}$$

-Given Data Set 1A, what is the median length of service?

A) 3 years.
B) 3.5 years.
C) 2 years.
D) 3 years..
E) 6 years.

Question 44

Data Set 1A
Suppose that the following table represents the length of service (in years) of the employees of a business: $$\begin{array} { l | l } \text { Number of } \\\text { Employees } & \text { Years } \\\hline 1 & 1 \\6 & 2 \\1 & 3 \\3 & 4 \\4 & 5\end{array}$$

-Given Data Set 1A, what is the modal length of service?

A) 4 years.
B) 6 years.
C) 5 years.
D) 3 years.
E) 3.5 years.

Question 45

Data Set 2A
Suppose that the ages of 8 kittens in a pet shop are as follows:
1, 2, 2, 3, 3, 4, 4, 5
What is the variance for Data Set 2A?

A) 1
B) 2
C) √1.5
D) 1.5
E) 2.5