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.

Accepted Answer

The sample may not be a random sample since only every tenth can is selected, which may not be representative of the entire production process. It is possible that the cans selected may have a different filling level than the rest of the cans. A truly random sample would involve selecting cans at random intervals rather than selecting every tenth can.

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.

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 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

Accepted Answer

B

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.

Accepted Answer

The answer of Data Set 1C
Suppose that the following table...

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.

Accepted Answer

To find the mean age, we add up all the ages and divide by the total number of houses. (10 + 8 + 5 + 7 + 3 + 6) / 6 = 5. Therefore, the mean age of the houses in the neighborhood is 5 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.

Accepted Answer

The Literary Digest poll relied on telephone surveys, which meant that it only included households with telephones. In 1936, many people could not afford a telephone, especially during the Great Depression, so the survey sample was not representative of the entire population. This resulted in a biased and inaccurate prediction of the election outcome.

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.

Accepted Answer

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

Question 8

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 measures of dispersion, which refer to how spread out a set of data is. Option D is the only choice that specifically refers to dispersion.

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.

Accepted Answer

This question involves a potentially sensitive topic for many people, so there is a possibility that some respondents may not wish to admit to having lied to their spouse. Because of this, it is likely that some people who have lied to their spouse will deny it, making the responses to this question untrustworthy.

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

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 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.

Accepted Answer

The answer of Suppose a poll is taken to sample...

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.

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 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.

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 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.

Accepted Answer

As the sample size increases, it becomes more representative of the population, reducing the likelihood of sampling error and increasing the accuracy of estimates.

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.

Accepted Answer

The answer of Suppose that the price of crude oil,...

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.

Accepted Answer

The wording of the question suggests that the concern is not about whether the respondents are reliable but rather that there is a potential for response bias. Since high school graduation is generally viewed as a positive thing, respondents may be more likely to answer "yes" even if they did not actually graduate from high school. This response bias could result in an overestimation of the number of high school graduates in the town. Therefore, option B is the best choice.

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.

Accepted Answer

While taking samples every day would provide a more comprehensive understanding of contaminant levels in the creek, taking random samples at intervals throughout one year could still provide valuable information about the presence of contaminants in the creek. The fact that the samples were taken from a single location in the center of the creek does limit the study in terms of spatial variation, but it still provides valuable information about contaminant levels at that location over time. Therefore, the survey could still be depended on to provide some insight into contaminant levels in the creek.

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.

Accepted Answer

By altering the vertical scale, the differences between the values are exaggerated or minimized, which can create a misleading impression of the true values. The horizontal scale should remain consistent to accurately reflect the data being presented. Altering both the horizontal and vertical scales by the same amount may maintain the relative proportions of the bars, but it still distorts the actual values. Narrowing the width of the bars or printing them in different colors may also visually exaggerate the differences but to a lesser extent than altering the vertical scale.

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.

Accepted Answer

The answer of Suppose two simultaneous random surveys were taken...

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.

Accepted Answer

Bias refers to a systematic error in the sampling process that leads to a sample that is not representative of the population. This can occur due to a variety of factors, such as using a non-random sampling method, having a small sample size, or having a sample that is not diverse enough. A biased sample can lead to inaccurate or misleading results when trying to make inferences about the population as a whole.

Quiz 12: Statistical Reasoning

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 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 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?

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

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?

Range, variance, and standard deviation are measurements of:

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?

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?

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?

In a normal distribution, the data represented are:

In general, the larger a sample is:

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 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?

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?

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

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