Question 1

Use the following information to answer questions (5) - (7). A tire manufacturer has made some
modifications to its most popular tire and wants to see if the tread on the modified tire will last
longer than the original tire. Because there is much variation in the way people drive, the
manufacturer decides to use blocking to reduce this variation. Twenty cars will be used to test the
tires. Ten cars are randomly selected to receive an original tire on the right rear wheel and a
modified tire on the left rear wheel. The remaining ten cars will receive an original tire on the left
rear wheel and a modified tire on the right rear wheel. Each car will then be driven 10,000 miles and
the amount of wear recorded for each wheel.
-Is this a correct use of blocking?

Accepted Answer

Blocking is used to reduce variation from extraneous factors, in this case, the variation in driving habits. By using each car to test both the original and modified tires, the experiment controls for differences in driving style, road conditions, and car type, which are all blocked by using the same car for both types of tires. This is a correct application of blocking.

Question 2

Which of the following statements is not true about a systematic sampling plan?

Accepted Answer

Systematic sampling does not divide the population into mini-populations with lower variability; instead, it involves selecting samples at regular intervals through the population.

Question 3

Use the following information to answer questions (5) - (7). A tire manufacturer has made some
modifications to its most popular tire and wants to see if the tread on the modified tire will last
longer than the original tire. Because there is much variation in the way people drive, the
manufacturer decides to use blocking to reduce this variation. Twenty cars will be used to test the
tires. Ten cars are randomly selected to receive an original tire on the right rear wheel and a
modified tire on the left rear wheel. The remaining ten cars will receive an original tire on the left
rear wheel and a modified tire on the right rear wheel. Each car will then be driven 10,000 miles and
the amount of wear recorded for each wheel.
-Was the study described above most likely an observational study or a controlled experiment?

Accepted Answer

The study is experimental because the researchers actively intervened by placing different types of tires on the cars and randomly assigning the position of these tires, thus controlling the conditions under which the tires were tested.

Question 4

Use the following information for following questions:. Which treatment is most effective at
treating carpet stains: vinegar, ammonia, or hydrogen peroxide? In a study, researchers randomly assigned
55 carpet samples with identical stains to one of three groups. Depending on which group they were
assigned to, each carpet sample received a home remedy of water mixed with vinegar, ammonia, or
hydrogen peroxide. Afterwards, each carpet sample was examined and any remaining stain was measured.
Researchers found that a vinegar and water mixture produced better results than both ammonia and
hydrogen peroxide.
-Choose the statement that restates the conclusion of the study in terms of a cause-and-effect conclusion.

Accepted Answer

The study directly compares the effectiveness of different treatments (vinegar, ammonia, hydrogen peroxide) and concludes that a water and vinegar mixture is more effective at treating carpet stains than the other options.

Question 5

A coin collector has over 54 books containing varying number of coins of various denominations. He is very interested in knowing the value of the collection, but does not want to take the time to look up the value of each coin in the collection. He decides to randomly select 4 books and determines the value of each coin in each of the 4 books by looking up the coin in an online pricing book. What kind of sampling does this illustrate?

Accepted Answer

This is an example of cluster sampling because the collector randomly selects entire books (clusters) and evaluates all coins within those selected books.

Question 6

In order to estimate the average amount of money due on 484 open accounts, the accountant at a large manufacturing company randomly selects 25 open accounts to audit. What kind of sampling does this illustrate?

Accepted Answer

This illustrates random sampling because the accountant selects a subset of accounts from the total population of open accounts at random, without following a specific order, grouping, or segmenting the accounts into clusters or strata.

Question 7

The quality control

Accepted Answer

A systematic sample of every 50th can throughout the day ensures that the sampling occurs at regular intervals over the entire production period, providing a comprehensive overview of the quality control process. This method is more representative of the entire production than selecting samples from specific time frames or using simple random samples that might miss systematic variations throughout the day.

Question 8

Which of the following is not a benefit of a stratified sampling plan?

Accepted Answer

Stratified sampling ensures that subgroups (strata) are adequately represented, but statistics from a single stratum do not necessarily reflect the parameters of the entire population. This method aims to increase overall sample precision and reduce variability within each stratum, not to make each stratum's statistics represent the whole population.

Question 9

The city council of a moderate size city wants to gather input from the citizens of the city on the proposed expansion to the local airport. It has been decided that a stratified sampling plan would be the best way to get the desired information because opinions within the strata are likely to be similar. Which method of stratifying seems to be the most reasonable for this situation?

Accepted Answer

Stratifying by distance from the airport is the most reasonable method because people living closer to the airport might have different opinions about its expansion compared to those living farther away, due to factors like noise and traffic.

Question 10

Which of the following is not an important principle that should always be kept in mind when reading research articles containing statistical research results?

Accepted Answer

Each of the options listed (A, B, and C) represents an important principle to consider when evaluating research articles containing statistical results.

Question 11

Use the following information for following questions:. A researcher wonders whether speed of
service at a diner is affected by whether a male customer is wearing a suit jacket. The researcher used the
following study design to collect data: The researcher chose five diners in a large city and recorded the
number of male customers who wore a suit jacket during a two week period. He also records how long it
took a waiter or waitress to address the customer. He finds that male customers who wear suit jackets
were addressed by the wait staff faster than male customers who did not wear a suit jacket.
-Choose the statement that correctly explains why we can or cannot make a cause-and-effect conclusion.

Accepted Answer

This was an observational study where the researcher simply observed and recorded behaviors without manipulating any variables. Without random assignment to control for other variables, we cannot definitively conclude causation.

Question 12

Which of the following is not a primary factor that affects the power of a test?

Accepted Answer

The primary factors that affect the power of a test include the size of the true difference between treatment groups, natural variability within the population, and sample size. The sample standard deviation is a measure of variability but is not considered a primary factor affecting power directly; rather, it's a component of natural variability.

Question 13

Suppose a sociologist is interested in finding out if there is an association between gender and opinions on human cloning. Which test design would be most appropriate for this scenario?

Accepted Answer

The Chi-square test is most appropriate for this scenario because it is used to determine if there is a significant association between two categorical variables, in this case, gender (male/female) and opinions on human cloning (e.g., support/oppose/neutral).

Question 14

Suppose it was reported on the news that a recent study concluded that the probability that you will get brain cancer if you use a cell phone doubled from 1 in 460,000 to 1 in 230,000. Choose the statement that best summarizes the significance of this result.

Accepted Answer

The doubling of the probability from 1 in 460,000 to 1 in 230,000, while statistically significant, represents a very small absolute increase in risk. This small absolute risk means the finding is unlikely to have a meaningful effect on most individuals' lives, indicating it lacks clinical significance despite its statistical significance.

Question 15

The personnel manager of a corporation wants to estimate, for one year, the total number of days used for sick leave among all 116 plants in his firm. The 116 plants are divided into 30 "small" plants, 45 "medium" plants, and 41 "large" plants. He decides to randomly select 40 employees from each of the three size of plants. What kind of sampling does this illustrate?

Accepted Answer

This is an example of stratified sampling because the personnel manager divides the plants into different strata (small, medium, and large) and then randomly selects a sample from each stratum.

Question 16

Suppose a gumball manufacturer decides to inspect every twenty-fifth gumball for defects. What kind of sampling does this illustrate?

Accepted Answer

Systematic sampling involves selecting samples based on a fixed interval, in this case, every twenty-fifth gumball, which is a characteristic of systematic sampling.

Question 17

Use the following information for following questions:. A researcher wonders whether speed of
service at a diner is affected by whether a male customer is wearing a suit jacket. The researcher used the
following study design to collect data: The researcher chose five diners in a large city and recorded the
number of male customers who wore a suit jacket during a two week period. He also records how long it
took a waiter or waitress to address the customer. He finds that male customers who wear suit jackets
were addressed by the wait staff faster than male customers who did not wear a suit jacket.
-Choose the statement that correctly explains why we can or cannot generalize these results to a larger population.

Accepted Answer

The study design described is observational and lacks random selection of male customers and diners from a larger population, which limits the ability to generalize the findings beyond the specific sample observed.

Question 18

Use the following information for following questions:. Which treatment is most effective at
treating carpet stains: vinegar, ammonia, or hydrogen peroxide? In a study, researchers randomly assigned
55 carpet samples with identical stains to one of three groups. Depending on which group they were
assigned to, each carpet sample received a home remedy of water mixed with vinegar, ammonia, or
hydrogen peroxide. Afterwards, each carpet sample was examined and any remaining stain was measured.
Researchers found that a vinegar and water mixture produced better results than both ammonia and
hydrogen peroxide.
-Was this a controlled experiment or an observational study?

Accepted Answer

This was a controlled experiment because the researchers actively intervened by randomly assigning each carpet sample to a treatment group (vinegar, ammonia, or hydrogen peroxide) and then measured the outcome (the effectiveness of the stain removal). This direct manipulation of the independent variable (type of treatment) to observe its effect on the dependent variable (stain removal) is characteristic of an experimental design.

Question 19

Use the following information to answer questions (5) - (7). A tire manufacturer has made some
modifications to its most popular tire and wants to see if the tread on the modified tire will last
longer than the original tire. Because there is much variation in the way people drive, the
manufacturer decides to use blocking to reduce this variation. Twenty cars will be used to test the
tires. Ten cars are randomly selected to receive an original tire on the right rear wheel and a
modified tire on the left rear wheel. The remaining ten cars will receive an original tire on the left
rear wheel and a modified tire on the right rear wheel. Each car will then be driven 10,000 miles and
the amount of wear recorded for each wheel.
-Which test design would be most appropriate for this scenario?

Accepted Answer

The design involves comparing two related samples (the original and modified tires on the same car), which is best analyzed using a paired t-test.

Question 20

Scientists were interested in determining if the amount of nicotine present in tobacco leaves is related to the amount of water received by the plants. In a greenhouse, a total of 120 tobacco plants were selected. During the growing season, 30 plants received the normal amount of water, 30 plants received 75% of the normal amount of water, 30 plants received 50% of the normal amount of water, and 30 plants received 25% of the normal amount of water. At the end of the growing season, one leaf was selected from each plant and the amount of nicotine present was recorded for each. Researchers determined that leaves from tobacco plants receiving the normal amount of water during the growing season had more nicotine than leaves from tobacco plants receiving less water. For this experiment, identify the response and treatment variables.

Accepted Answer

The response variable is what is measured or observed in response to changes or variations in the treatment variable. In this experiment, the amount of nicotine in the leaf is measured as a response to varying the amount of water the plants receive, making the amount of nicotine the response variable and the amount of water the treatment variable.

Quiz 12: Experimental Design: Controlling Variation