Question 1

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?

Accepted Answer

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. 
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. B

Question 2

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?

Accepted Answer

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. 
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. D

Question 3

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?

Accepted Answer

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

Question 4

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?

Accepted Answer

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. 
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 5

The range of a set of data is:

Accepted Answer

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. 
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 6

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?

Accepted Answer

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. 
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 7

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?

Accepted Answer

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

Question 8

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

Accepted Answer

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. 
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 9

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

Accepted Answer

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. 
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 10

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?

Accepted Answer

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

Question 11

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?

Accepted Answer

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. 
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 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?

Accepted Answer

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

Question 13

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,

Accepted Answer

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. 
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 14

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?

Accepted Answer

A)  √2 
B)  1 
C)  1.5 
D)  2 
E)  √1.5 
A)  √2 
B)  1 
C)  1.5 
D)  2 
E)  √1.5

Question 15

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?

Accepted Answer

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. 
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 16

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

Accepted Answer

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. 
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 17

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?

Accepted Answer

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%. 
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 18

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?

Accepted Answer

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

Question 19

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,

Accepted Answer

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. 
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.

Question 20

In general, the larger a sample is:

Accepted Answer

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. 
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.

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?

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?

Data Set 1B Suppose that the following table represents the age of the cars in a small used car lot: Number of Cars Age 2 1 4 2 1 3 5 4 1 6 -Given Data Set 1B, what is the mean age of the cars?

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?

The range of a set of data is:

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?

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?

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

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

Data Set 1A Suppose that the following table represents the length of service (in years) of the employees of a business: Number of Employees Years 1 1 6 2 1 3 3 4 4 5 -Given Data Set 1A, what is the median length of service?

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?

Data Set 1C Suppose that the following table represents the age of the houses in a certain neighborhood: Number of Houses Age 2 1 5 3 1 4 3 6 4 9 -Given Data Set 1C, what is the modal age of the houses?

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,

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?

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

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?

Data Set 1A Suppose that the following table represents the length of service (in years) of the employees of a business: Number of Employees Years 1 1 6 2 1 3 3 4 4 5 -Given Data Set 1A, what is the modal length of service?

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,

In general, the larger a sample is:

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Exam 12: Statistical Reasoning

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?

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?

Data Set 1B Suppose that the following table represents the age of the cars in a small used car lot: Number of Cars Age 2 1 4 2 1 3 5 4 1 6 -Given Data Set 1B, what is the mean age of the cars?

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?

The range of a set of data is:

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?

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?

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

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

Data Set 1A Suppose that the following table represents the length of service (in years) of the employees of a business: Number of Employees Years 1 1 6 2 1 3 3 4 4 5 -Given Data Set 1A, what is the median length of service?

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?

Data Set 1C Suppose that the following table represents the age of the houses in a certain neighborhood: Number of Houses Age 2 1 5 3 1 4 3 6 4 9 -Given Data Set 1C, what is the modal age of the houses?

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,

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?

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

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?

Data Set 1A Suppose that the following table represents the length of service (in years) of the employees of a business: Number of Employees Years 1 1 6 2 1 3 3 4 4 5 -Given Data Set 1A, what is the modal length of service?

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,

In general, the larger a sample is:

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Propositional Logic

Natural Deduction in Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Hypotheticalscientific Reasoning

Science and Superstition

Filters