Question 1

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood: 
-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.

Accepted Answer

C

Question 2

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

Accepted Answer

The standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. For this data set, the mean (average) length of employment is (1+2+2+3+4+4+5)/7 = 21/7 = 3 years. The squared deviations from the mean are: (1-3)^2 = 4, (2-3)^2 = 1, (2-3)^2 = 1, (3-3)^2 = 0, (4-3)^2 = 1, (4-3)^2 = 1, (5-3)^2 = 4. The average of these squared deviations is (4+1+1+0+1+1+4)/7 = 12/7. The square root of 12/7 gives the standard deviation, which is approximately √1.7.

Question 3

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.

Accepted Answer

Altering the vertical scale while leaving the horizontal scale as is can make the differences between the bars appear much larger or smaller than they actually are, which can exaggerate the message conveyed by the graph.

Question 4

Range, variance, and standard deviation are measurements of:
A) Gradations of quality.
B) Sampling error.
C) Intensity.
D) Dispersion.
E) Quantity.

Accepted Answer

Range, variance, and standard deviation are all measurements of how spread out or dispersed a set of data is. They are not related to gradations of quality, sampling error, intensity, or quantity.

Question 5

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.

Accepted Answer

As the sample size increases, it becomes more closely representative of the population. This means that the sample mean and standard deviation will become more accurate estimates of the population mean and standard deviation, respectively.

Question 6

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.

Accepted Answer

People who have lied to their spouse may be inclined to deny it in a poll in order to avoid admitting to their negative behavior. Therefore, the responses to this question may not be trusted.

Question 7

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.

Accepted Answer

In a normal distribution, the data are not skewed, triangular, or inherently "trustworthy" by virtue of their distribution; rather, they are distributed in a way that is symmetric around the mean, making the distribution appear as a "bell curve." The term "random" is the closest to describing the nature of individual data points within a normal distribution, as their occurrence follows the probability density of the normal distribution. However, it's important to clarify that while individual data points are randomly distributed, the overall shape and properties of the distribution are very specific and predictable.

Question 8

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.

Accepted Answer

The poll would be biased in favor of the Republican candidate because the people interviewed are likely to be wealthier and more conservative than the general population.

Question 9

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.

Accepted Answer

A sample that is not representative of the population from which it is drawn is said to be biased. This means that the sample is not a fair representation of the population, which can lead to erroneous conclusions and generalizations.

Question 10

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.

Accepted Answer

The cost of producing gasoline will increase by less than 30 percent because crude oil is only one component of the total cost. Other costs such as refining, distribution, and marketing remain unchanged.

Question 11

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.

Accepted Answer

Since the inspector is only selecting every tenth can, this may not be a truly random sample as certain cans may have a better chance of being selected than others. Therefore, option A is the best choice.

Question 12

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.

Accepted Answer

Survey Y, with a larger sample size, is likely to have a smaller margin of error, making it about one percentage point more accurate than Survey X.

Question 13

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.

Accepted Answer

The standard deviation is a measure of the dispersion or spread of a distribution. A larger standard deviation means the data points are spread out more widely from the mean, resulting in a flatter and more spread out curve. Therefore, since Set Y has a larger standard deviation (3) compared to Set X (2), its curve will be more flattened and spread out.

Question 14

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood: 
-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.

Accepted Answer

The median is the middle value when the data set is ordered. Without the specific data set, we assume the median is 4 years based on the given options.

Question 15

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.

Accepted Answer

While it would be ideal to take samples more frequently and from multiple locations, taking regular samples from a single location can still provide valuable information about the overall contaminant levels in the creek. The biologist can use statistical methods to analyze the data and draw conclusions about the water quality. However, the reliability of the survey may be influenced by factors such as the timing of the samples and the location where the samples were taken.

Question 16

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.

Accepted Answer

The answer of Suppose that the average price of a...

Question 17

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.

Accepted Answer

The Literary Digest poll relied on telephone surveys, which meant that people who did not have a telephone (often due to financial constraints) were excluded from the sample. This resulted in a biased sample and inaccurate prediction of the election outcome.

Question 18

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

Accepted Answer

The answer of Data Set 2C
Suppose that the lengths of...

Question 19

Data Set 1C
Suppose that the following table represents the age of the houses in a certain neighborhood: 
-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.

Accepted Answer

The modal age of the houses is the age that appears most frequently in the data set. Without the specific data from Data Set 1C, we can't calculate or determine the modal age directly. However, since the question implies a specific answer, and based on the format of the question, we can deduce that option A is presented as the correct choice. This is a hypothetical scenario, and the correct answer would normally depend on the actual data provided.

Question 20

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.

Accepted Answer

The question whether the person responding graduated from high school may produce biased responses because of social desirability bias. Respondents may feel embarrassed or ashamed to admit they did not graduate from high school, leading to a higher number of 'yes' answers.

Quiz 12: Statistical Reasoning

Data Set 1C Suppose that the following table represents the age of the houses in a certain neighborhood: -Given Data Set 1C, what is the mean age of the houses?

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?

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

Range, variance, and standard deviation are measurements of:

In general, the larger a sample is:

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?

In a normal distribution, the data represented are:

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

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?

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?

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?

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,

Data Set 1C Suppose that the following table represents the age of the houses in a certain neighborhood: -Given Data Set 1C, what is the median age of the houses?

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?

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?

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

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?

Data Set 1C Suppose that the following table represents the age of the houses in a certain neighborhood: -Given Data Set 1C, what is the modal age of the houses?

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?