Algebra II : Experiment Design and Identifying Bias
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : Experiment Design And Identifying Bias
No
Yes
No
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 #2 : 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?
Yes
No
Yes
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 #3 : Experiment Design And Identifying Bias
No
Yes
Yes
Example Question #2 : Experiment Design And Identifying Bias
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?
Yes. The student and her friends called all 400 students in his high school, excluding none.
No. Some calls were not answered.
No. The mothers of students at her school are not likely to be representative of mothers in the city as a population.
Yes. The answers recorded correctly reflect the number of calls made and answered.
No. The mothers of students at her school are not likely to be representative of mothers in the city as a population.
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 #82 : 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?
Yes. Providing both groups with a treatment is fair.
Yes. Placebos help to verify whether an experimental treatment is effective.
No. Only one group should receive any kind of treatment.
No. It is unethical to provide placebo treatments to human participants.
Yes. Placebos help to verify whether an experimental treatment is effective.
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 #83 : 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?
Blind
Subjective
Double-blind
Observational
Blind
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 #84 : 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?
Blind
Subjective
Double-blind
Observational
Double-blind
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?
The social media company
Users targeted with the old slogans
Users targeted with the new slogans
The researcher
Users targeted with the old slogans
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 #2 : 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 experimental group?
Users targeted with the new slogans
Users targeted with the old slogans
The social media company
The researcher
Users targeted with the new slogans
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 #8 : 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. 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:
Is her conclusion correct?
Yes. The new ads have more clicks than the old ads.
No. The old ads have fewer clicks than the new ads.
No. The results are not statistically significant.
Yes. The results are statistically significant.
No. The results are not statistically significant.
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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