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MATH 225N Week 8 Assignment; Correlation and Causation

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1. Question: True or False: The more samples taken in a scientific study, the longer the amount of time it will take to complete the research on the samples.Although there are other factors that affect study time, such as experience and equipment, increasing the number of samples will cause an increase in research time. 2. Question: Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.) 3. Question: Which of the following situations could have a regression line with a negative y-intercept? Select all that apply: 4. Question: Which of the following data sets or plots could have a regression line with a negative slope? Select all that apply. 5. Question: Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information. 6. Question: An experiment finds that runners with the longest legs complete a mile run in less time.Identify the relation between leg length and time of a mile run.Leg length and time of a mile run are negatively correlated. A longer leg length is associated with a lower time of a mile run, which implies a negative relationship. There would need to be more evidence to prove causation. 7. Question: Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply. 8. Question: Which of the following situations could produce data sets or plots would have a regression line with a negative slope? Select all that apply.

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Week 8 Assignment: Correlation and Causation
Understand the difference between correlation and causation

Question
True or False: The more samples taken in a scientific study, the longer the amount
of time it will take to complete the research on the samples. Although there are
other factors that affect study time, such as experience and equipment, increasing
the number of samples will cause an increase in research time. Correct! You
nailed it.
Understand the difference between correlation and causation

Question
Suppose that a large controlled experiment tests whether caffeine improves
reaction times. A very large number of randomly selected participants are
randomly given identical-seeming pills with varying doses of caffeine (including
none) and then given tests of reaction times under the same conditions. The
experiment finds a strong negative correlation between caffeine dose and reaction
time. (Note that lower reaction times are better.) Correct answer:
There is evidence that caffeine causes lower (better) reaction times.
Correlation alone does not prove causation, but this scenario provides more
evidence than just correlation between two variables. Since the data were obtained
from an appropriately randomized controlled experiment, a correlation can be
used as evidence of a causal relationship. Since all other variables were controlled,
there is no third variable that could be associated with caffeine that actually causes
differences in reaction times. Yes that's right. Keep it up!
Interpret the slope and y-intercept of the least squares regression line

Question
Which of the following situations could have a regression line with a negative y-
intercept?

Select all that apply: Great work! That's correct.

 The present value of an insurance policy as a function of the age of the ensured
person if the person purchases the policy when he or she is 50 years old.



 The number of millions of barrels of oil in an oil field as a function of the number of
years the oil field has been in production.

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