Reaction time studies are studies in which participants receive a stimulus and t
ID: 3071945 • Letter: R
Question
Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screen. When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when the participant clicked the button.
Suppose that, in these tests, the distribution of reaction times is skewed slightly to the right. Suppose also that mean reaction time is 190 milliseconds, and the standard deviation for reaction times is 20 milliseconds (for the purposes of this problem, you can treat the mean and standard deviation as population parameters). Use this information to answer the following questions, and round your answers to four decimal places.
a. Suppose we have 12 different people take this reaction time test. What is the probability that the average of these 12 reaction times will be greater than 181 milliseconds?
b. Suppose we have 16 different people take this reaction time test. What is the probability that the average of these 16 reaction times will be less than 195 milliseconds?
c. Suppose we have 25 different people take this reaction time test. What is the probability that the average of these 25 reaction times will be less than 182 milliseconds?
d. Would it be appropriate to use the normal probability app to compute the probability that a single reaction time is less than 182 milliseconds? (You have two attempts for this question.)
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Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screern When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when the participant clicked the button. Suppose that, in these tests, the distribution of reaction times is skewed slightly to the right. Suppose also that mean reaction time is 190 milliseconds, and the standard deviation for reaction times is 20 milliseconds (for the purposes of this problem, you can treat the mean and standard deviation as population parameters). Use this information to answer the following questions, and round your answers to four decimal places. a. Suppose we have 12 different people take this reaction time test. What is the probability that the average of these 12 reaction times will be greater than 181 milliseconds? b. Suppose we have 16 different people take this reaction time test. What is the probability that the average of these 16 reaction times will be less than 195 milliseconds? C. Suppose we have 25 different people take this reaction time test. What is the probability that the average of these 25 reaction times will be less than 182 milliseconds? d. Would it be appropriate to use the normal probability app to compute the probability that a single reaction time is less than 182 milliseconds? (You have two attempts for this question.) O Yes, because the Central Limit Theorem makes everything become normally distributed O No, because reaction times are not normally distributed, and the normal probability app is only for computing probabilities associated with a normally distributed variable O Yes, because converting a variable to a z-score makes that variable become normally distributed O No, because we can only compute the probability that reaction time is less than *or equal to* 182 milliseconds. O Yes, because everything in statistics is an approximation and so it doesn't matter if our methodology makes sense All that matters is that we use a method that produces a number of some sort. O Yes, because the Law of Large Numbers states that as a variable increases, it becomes more accurate O No, because you cannot compute a probability for a single event, only for the long run relative frequency of an infinite number of eventsExplanation / Answer
Answer:
Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screen. When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when the participant clicked the button.
Suppose that, in these tests, the distribution of reaction times is skewed slightly to the right. Suppose also that mean reaction time is 190 milliseconds, and the standard deviation for reaction times is 20 milliseconds (for the purposes of this problem, you can treat the mean and standard deviation as population parameters). Use this information to answer the following questions, and round your answers to four decimal places.
a. Suppose we have 12 different people take this reaction time test. What is the probability that the average of these 12 reaction times will be greater than 181 milliseconds?
Standard error = sd/sqrt(n) =20/sqrt(12) =5.7735
z value for 181, z = (181-190)/5.7735 = -1.56
P( mean x > 181) = P( z > -1.56)
=0.9406
b. Suppose we have 16 different people take this reaction time test. What is the probability that the average of these 16 reaction times will be less than 195 milliseconds?
Standard error = sd/sqrt(n) =20/sqrt(16) =5
z value for 195, z = (195-190)/5.0 = 1
P( mean x < 195) = P( z < 1)
=0.8413
c. Suppose we have 25 different people take this reaction time test. What is the probability that the average of these 25 reaction times will be less than 182 milliseconds?
Standard error = sd/sqrt(n) =20/sqrt(25) =4
z value for 182, z = (182-190)/4.0 = -2
P( mean x < 182) = P( z < -2)
=0.0228
d. Would it be appropriate to use the normal probability app to compute the probability that a single reaction time is less than 182 milliseconds? (You have two attempts for this question.)
Yes, because the Central Limit Theorem makes everything become normally distributed.
Answer: No, because reaction times are not normally distributed, and the normal probability app is only for computing probabilities associated with a normally distributed variable.
Yes, because converting a variable to a z-score makes that variable become normally distributed.
No, because we can only compute the probability that reaction time is less than *or equal to* 182 milliseconds.
Yes, because everything in statistics is an approximation and so it doesn't matter if our methodology makes sense. All that matters is that we use a method that produces a number of some sort.
Yes, because the Law of Large Numbers states that as a variable increases, it becomes more accurate.
No, because you cannot compute a probability for a single event, only for the long run relative frequency of an infinite number of events.
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