Reaction time studies are studies in which participants receive a stimulus and t

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 thern 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 8 different people take this reaction time test. What is the probability that the average of these 8 reaction times will be greater than 180 milliseconds? b. Suppose we have 14 different people take this reaction time test. What is the probability that the average of these 14 reaction times will be less than 191 milliseconds? C. Suppose we have 30 different people take this reaction time test. What is the probability that the average of these 30 reaction times will be less than 184 milliseconds? d. Would it be appropriate to use the normal probability app to compute the probability that a single reaction time is less than 184 milliseconds? (You have two attempts for this question.) 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 the Central Limit Theorem makes everything become normally distributed 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 converting a variable to a z-score makes that variable O No, because you cannot compute a probability for a single event, only for o Yes, because the Law of Large Numbers states that as a variable O No, because we can only compute the probability that reaction time is become normally distributed. the long run relative frequency of an infinite number of events. increases, it becomes more accurate less than or equal to 184 milliseconds.

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =20/(8)1/2 =7.07

therefore probability =P(X>180) =P(Z>(180-190)/7.07)=P(Z>-1.4142)=0.9214

b)

std error of mean =std deviation/(n)1/2 =20/(14)1/2 =5.3452

therefore probability =P(X<191) =P(Z<(191-190)/5.3452)=P(Z<0.1871)=0.5742

c)

std error of mean =std deviation/(n)1/2 =20/(30)1/2 =3.6515

therefore probability =P(X<184) =P(Z<(184-190)/3.6515)=P(Z<-1.6432)=0.0502

d) option 1st

No because reaction times are not normally distributed ..........

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