Reaction time studies are studies in which partikcipants receive a stimulus and

Question

Reaction time studies are studies in which partikcipants 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 partiipant holds a clickor button and stares at a screen. When the participant seos a part of the screen light up, he or she dlicks the button as quickly as possible. The researcher then records bow much time elapsed between when the screen Iit up and when the participant clicked the button. Suppose that, in these tests, the distrilbution of reaction times is skewed slightly to the right. Suppose also that mean reaction tieme is 190 milliseconds, and the standard deviatien for reacion 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 we have 11 different people take this reaction time test. What is the probability that the average of these 11 reacdtion tmes wil be greater than 182 meliseconds b. Suppose we have 13 different people take this reaction time test. What is the probablity that the average of these 13 reaction times will be less than 196 miliseconds C Suppose we have 27 dfferent people take this reaction time test, What is the probability that the average of these 27 reaction tmes will be less than 189 mis d woulan be appropriate to use the no ma probab ty app to compute tho probability thatsingle reaction time is less than·89 miliseconds, You have two attempts for thi question) Yes,because the La of Large Numbers states that as a variable increases, becomes more accurate No, because you cannot compute a probablity for a single event, only for the long nun relative frequency of an infinite number of events Yes, because converting a variable to a z.score makes that variable become normally distributed. res, because the Central Limit Theorem makes everything become normally distributed No,because we can only compute the probability that reaction time is less than "or equal to" 189 miiseconds es, because everything in statistics is an approximation and so it doesn't matter if our methodology makes sense All hat matters is that we use a method that produces sumber of some sot No, because reaction me are not nomally stributed and the mal probability app is only for computing probabiiries assocated with a nemally distribsted varlable,

Explanation / Answer

SolutionA:

mean=190

sd=20

n=11

P(X bar>182)

z=x-mean/sd/sqrt(n)

=182-190/20/sqrt(!1)

=-8/20/sqrt(11)

=-1.33

P(X bar.>182)

=P(Z>-1.33)

=0.9082

ANSWER:0.9082

Solutionb:

P(X bar<196)

n=13

z=196-190/20/sqrt(13)

z=1.08

P(Z<1.08)

=0.8599

ANSWER:0.8599

Solutionc:

n=27

P(X bar<189)

z=189-190/20/sqrt(27)

z=-0.26

P(Z<-0.26)

pnorm(-0.26)

=0.3974

ANSWER:0.3974

Solutiond:

yes because central limit theroem makes evrything normally distributed

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.