udy examining the effect of alcohol on reaction Liguori and Robinson (2001) foun

Question

udy examining the effect of alcohol on reaction Liguori and Robinson (2001) found that even ex 14. In a time, moderate alcohol consumption significantly slowed time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a dardized driving simulation task for which the regular population averages -400msec. The distribution of reaction times is approximately normal with = 40. Assume that the researcher obtained a sample mean of M = 422 for the n = 25 participants in the study. a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with = .01. b. Do the data provide evidence that the alcohol significantly increased (slowed) reaction time? Use a one-tailed test with = .01. Compute Cohen's d to estimate the size of the c. effect. 15. The researchers cited in the previous problem (Liguori and Robinson, 2001) also examined the effect of caf- feine on response time in the driving simulator. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce cup of coffee. Using the same driving simulation task, for which the distribution of reaction times is normal with = 400 msec and = 40, they obtained a mean of 11-392 for a sample of n = 36 participants. a. Are the data sufficient to conclude that caffeine has a significant effect on reaction time? Use a two- tailed test with .05. b. Compute Cohen's d to estimate the size of t effect. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

Explanation / Answer

Q14.

Given that,

population mean(u)=400

standard deviation, =40

sample mean, x =422

number (n)=25

null, Ho: =400

alternate, H1: !=400

level of significance, = 0.01

from standard normal table, two tailed z /2 =2.576

since our test is two-tailed

reject Ho, if zo < -2.576 OR if zo > 2.576

we use test statistic (z) = x-u/(s.d/sqrt(n))

zo = 422-400/(40/sqrt(25)

zo = 2.75

| zo | = 2.75

critical value

the value of |z | at los 1% is 2.576

we got |zo| =2.75 & | z | = 2.576

make decision

hence value of | zo | > | z | and here we reject Ho

p-value : two tailed ( double the one tail ) - ha : ( p != 2.75 ) = 0.00596

hence value of p0.01 > 0.00596, here we reject Ho

ANSWERS

---------------

null, Ho: =400

alternate, H1: !=400

test statistic: 2.75

critical value: -2.576 , 2.576

decision: reject Ho

p-value: 0.00596

a.

alohocal consumption significantly slowed response response time to

an emergencey situation

b.

critical value

the value of |z | at los 1% is 2.326

we got |zo| =2.75 & | z | = 2.326

make decision

hence value of | zo | > | z | and here we reject Ho

p-value : right tail - ha : ( p > 2.75 ) = 0.00298

hence value of p0.01 > 0.00298, here we reject Ho

ANSWERS

---------------

null, Ho: =400

alternate, H1: >400

test statistic: 2.75

critical value: 2.326

decision: reject Ho

p-value: 0.00298

we have evidence that alcohal significantly increased

c.

d = (x µ) /

x = sample mean

µ = null hypothesis population mean

= null hypothesis population standard deviation

= (422 - 400) / 40

= 0.55

Interpreting Cohen's d

d = 0.2 Small effect - mean difference is 0.2 standard deviation

d = 0.5 Medium effect - mean difference is 0.5 standard deviation

d = 0.8 Large effect - mean difference is 0.8 standard deviation

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