Algebra II : Experiment Design and Identifying Bias

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #5172 : Algebra Ii

Medical data shows it can take more than 4 months to recover from knee replacement surgery. A team of researchers is conducting an experiment to see if a new rehabilitation program can help reduce this time. The researchers ask 80 randomly chosen knee replacement patients to use the new program. They then note the recovery time for each patient.
 
Is this a statistically well designed experiment?
Possible Answers:

Yes

No

Correct answer:

No

Explanation:

No, this experiment is not statistically well designed. In order to be statistically well designed, an experiment's subjects must be randomly sorted into two groups (experimental and control), everyone in the experimental group gets the experiment, and everyone in the control group does not get the experiment. All 80 participants were asked only to participate in the experimental trial; no one was placed into a control group. For this reason, this experiment is not statistically well designed.

Example Question #1 : Experiment Design And Identifying Bias

Krystal owns a boutique clothing store, and wants to learn more about her customers. She sends out a survey to the 35 customers who spent the most money in her store last month. Is this sample of customers likely to be biased?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

Yes, this sample is likely to be biased. If Krystal only reaches out to the customers who spent the most money, she may fail to understand all types of consumer habits. 

Example Question #86 : Probability

Miko is a psychologist conducting a study about biased grading. She wants to see whether English teachers will give a paper a higher grade if they have just graded a poorly written paper.
Miko recruits 30 teachers for the study and randomly sorts them into two groups. She has the 115 teachers in one group grade a poorly written paper, and the other 15 teachers grade an average paper. Afterward, all 30 teachers are given the same paper to grade. Miko records the grades for this paper.
 
Is this experiment statistically well designed?
Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:
Yes, this experiment is statistically well designed. In order to be statistically well designed, an experiment's subjects must be randomly sorted into two groups (experimental and control), everyone in the experimental group gets the experiment, and everyone in the control group does not get the experiment. Miko randomly sorted the teachers. Fifteen of them saw a poor paper (experiment) and fifteen saw an average paper (control). Afterwards, they were all given an identical paper to grade. While we don't know what the quality of that final identical paper was, the quality itself does not matter, but rather, how each of the 30 individuals grade it, and whether those in the experimental group do so differently than those in the control group IS what matters. Because the experiment has an experimental group and a control group, and both groups were randomly chosen, the experiment is statistically well designed.

Example Question #87 : Probability

A student wants to find out whether mothers in his city support a local initiative to redesign the city’s largest park. He decides to conduct a poll on this question by calling the home phone numbers of all 200 students in his private high school, asking to speak to their mothers, and recording their responses as YES, NO or NO PREFERENCE in a chart. He doesn’t have time to make 400 calls, so he enlists three friends, who are also students at his school, to help make calls and record answers. 

100 calls are not answered, and during 50 calls no mothers are home. The remaining 250 calls successfully reach mothers: 200 of the 250 calls are recorded as YES, 25 are recorded as NO and 25 are recorded as NO PREFERENCE. The student concludes that most mothers in the city support the initiative.

Which of the following best describes whether this study is well-designed, and why?

 

Possible Answers:

Yes. The answers recorded correctly reflect the number of calls made and answered.

No. Some calls were not answered.

Yes. The student and her friends called all 400 students in his high school, excluding none.

No. The mothers of students at her school are not likely to be representative of mothers in the city as a population.

Correct answer:

No. The mothers of students at her school are not likely to be representative of mothers in the city as a population.

Explanation:

Given the small population of students at the high school, it is highly unlikely that all mothers in the city are represented in the sample; and given that the high school is both small and private, it is unlikely that the sample is representative of all mothers in the city, creating sampling bias.

Example Question #88 : Probability

A researcher seeks to test the effectiveness of an experimental treatment for strep throat. She randomly divides her study participants, all of whom have been diagnosed with strep throat, into two groups: one group receives the experimental treatment. 

Should the other group receive a placebo treatment?

 

 

Possible Answers:

Yes. Providing both groups with a treatment is fair.

 

No. Only one group should receive any kind of treatment.

Yes. Placebos help to verify whether an experimental treatment is effective.

No. It is unethical to provide placebo treatments to human participants.

Correct answer:

Yes. Placebos help to verify whether an experimental treatment is effective.

Explanation:

It is well documented that when people believe they are receiving a treatment, they experience what they expect will be the effects of that treatment. Placebos help to verify whether an experimental treatment is effective by reducing the likelihood that study participants’ expectations or beliefs about treatments, or about whether they received a treatment, skew study results. 

 

 

Example Question #89 : Probability

A researcher seeks to test the effectiveness of an experimental treatment for strep throat. She randomly divides her study participants, all of whom have been diagnosed with strep throat, into two groups: one group receives the experimental treatment, while the other receives a placebo treatment. No study participant is told whether he or she has received the experimental treatment or the placebo, but the researcher keeps careful track of which participants have received the experimental treatment and which have not. 

What is the design of this study?

 

 

Possible Answers:

Double-blind

Observational

Subjective

Blind

Correct answer:

Blind

Explanation:

It is well documented that when people believe they are receiving a treatment, they experience what they expect will be the effects of that treatment.  In a blind study, no participant being studied is aware which group he or she is in, or exactly what treatment he or she received. This can help prevent study participants’ expectations and beliefs about treatments, or about whether they received a treatment, from skewing study results.

Example Question #90 : Probability

A researcher seeks to test the effectiveness of an experimental treatment for strep throat. She randomly divides her study participants, all of whom have been diagnosed with strep throat, into two groups: one group receives the experimental treatment, while the other receives a placebo treatment. During the study, neither the researcher nor the study participants know who has received the experimental treatment, and who has received the placebo.

What is the design of this study?

 

 

Possible Answers:

Double-blind

Blind

Subjective

Observational

Correct answer:

Double-blind

Explanation:

When researchers are aware which study participants have received which treatments, they may consciously or subconsciously behave in ways that skew results of the study towards the researchers’ own perspectives or interests. In a double-blind study, during the study neither the researchers nor any participant is aware which group he or she is in, or exactly what treatment he or she received. This can prevent researcher behavior from skewing study results.

Example Question #1 : Experiment Design And Identifying Bias

A marketer is piloting a set of new advertisement slogans--a potential replacement for her company’s old slogans--to determine the new slogans’ effectiveness at raising the number of clicks her ads receive. She partners with a social media company to test the slogans by targeting 1,000 random social media users each day with the new slogans and targeting 1,000 different random users each day with the old slogans. 

Which of the following is the control group?

 

 

Possible Answers:

Users targeted with the old slogans

The social media company

Users targeted with the new slogans

The researcher

Correct answer:

Users targeted with the old slogans

Explanation:

The control group in an experiment does not receive the experimental treatment, but resembles the group receiving the experimental treatment. Thus, the dependent variable associated with the control group is not affected by the independent variable in the experiment. This allows the researcher to compare the effect of the experimental treatment on the experimental group with the effect of no treatment, making the effect of the treatment easier to verify.

Example Question #92 : Probability

A marketer is piloting a set of new advertisement slogans--a potential replacement for her company’s old slogans--to determine the new slogans’ effectiveness at raising the number of clicks her ads receive. She partners with a social media company to test the slogans by targeting 1,000 random social media users each day with the new slogans and targeting 1,000 different random users each day with the old slogans. 

Which of the following is the experimental group?

 

 

Possible Answers:

Users targeted with the new slogans

Users targeted with the old slogans

The researcher

The social media company

Correct answer:

Users targeted with the new slogans

Explanation:

The experimental group in an experiment receives the experimental treatment. The dependent variable associated with the experimental group is affected by the independent variable in the experiment, while the dependent variable associated with the control group is not. 

 

 

Example Question #93 : Probability

A marketer is piloting a set of new advertisement slogans--a potential replacement for her company’s old slogans--to determine the new slogans’ effectiveness at raising the number of clicks her ads receive. She partners with a social media company to test the slogans by targeting 1,000 random social media users each day with the new slogans and targeting 1,000 different random users each day with the old slogans. When the study ends, she compares the click activity on ads with each type of slogan and concludes that the new slogans are effective.

The results are represented in the table below:

Screen shot 2020 08 25 at 4.16.06 pm

Is her conclusion correct?

Possible Answers:

No. The results are not statistically significant.

Yes. The results are statistically significant.

No. The old ads have fewer clicks than the new ads.

Yes. The new ads have more clicks than the old ads.

Correct answer:

No. The results are not statistically significant.

Explanation:

A statistically significant result of an experiment is one in which a change in the experimental group’s dependent variable is attributable to a change in the independent variable. In other words, a statistically significant result in a well designed experiment is one that is large enough in scale that it is unlikely to be a result of mere chance. In the table provided, the difference between the total ad clicks resulting from each of the slogan types is minuscule--a difference of only 3 clicks out of over 2,000 for each type. This suggests that the results may simply have been the result of chance, since the difference in total clicks is so small in scale that it is difficult to clearly attribute to the change in slogan types.

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