Algebra 2 Problems of the Day

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August 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


16. A study conducted in 2004 in New York City found that 212 out of 1334 participants had hypertension. Kim ran a simulation of 100 studies based on these data. The output of the simulation is shown in the diagram below.

At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to

1) proportion ≈ .16; margin of error ≈.01
2) proportion ≈ .16; margin of error ≈.02
3) proportion ≈ .01; margin of error ≈.16
4) proportion ≈ .02; margin of error ≈.16

Answer: 2) proportion ≈ .16; margin of error ≈.02
Hopefully, it's "obvious" from the choices that the proportion is approximately .16, not .01 or .02. And the margin of error is not .16.
The question is, which is the margin of error, .01 or .02?

You can find the margin of error for proportions using the formula
ME = z( sqrt( ((p)(1-p))/n ) ),
where p is the proportion, n is the number of participants and z is the z-score, which 1.96 for 95% confidence.

So ME = (1.96)( sqrt( ((0.16)(0.84))/1334 ) ) = 0.019673... or about 0.02.

17. Which scenario is best described as an observational study?

1) For a class project, students in Health class ask every tenth student entering the school if they eat breakfast in the morning.
2) A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.
3) A researcher wants to learn whether or not there is a link between children's daily amount of physical activity and their overall energy level. During lunch at the local high school, she distributed a short questionnaire to students in the cafeteria
4) Sixty seniors taking a course in Advanced Algebra Concepts are randomly divided into two classes. One class uses a graphing calculator all the time, and the other class never uses graphing calculators. A guidance counselor wants to determine whether there is a link between graphing calculator use and students' final exam grades.

Answer: 2) A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.
An observational study draws inferences from a sample where the independent variable is not under the control of the researcher. In the second scenario, the researcher is removed from the subjects of the study. In choices 1 and 3, there is interaction between the researcher and the subjects. In choice 4, preventing students from using calculators to see if it affects their final exam grades wouldn't be an ethical study.

18. Which sinusoid has the greatest amplitude?

Answer:4) y = −5sin(θ − 1) − 3
You can see from the graphs that Choice 3 has a greater amplitude than Choice 1, which we can eliminate.
You can see from the values in front of the equations, 3 and -5, that Choice 4 has a greater amplitude than Choice 2, which we can eliminate.
Choice 4 has an Amplitude of 5. Choice 2 has an Amplitude of 8/2 = 4. (You need to divide it by 2 because the amplitude is measured from the center line, not top to bottom.)



Comments and questions welcome.

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