An experiment was conducted to test effects of alcohol. The errors were recorded

Question

An experiment was conducted to test effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group who drank alcohol and another group given a placebo. Treatment group: n=22, xbar=4.2, s=2.2 Placebo group: n=22, xbar=1.71, s=0.72 Use 0.05 significance level to test claim that there is a difference between the treatment group and placebo group. Show graphs Does drinking alcohol affect visual and motor skills? (explain your answer based on original claim) Construct 95% confidence interval estimates of the difference between two population means. Do the results support the common belief that drinking alcohol is hazardous for drivers, pilots, ship captains, and so on? Why or why not?

Explanation / Answer

n1 =22, x1bar = 4.2 ,s1 = 2.2

n2 =22 x2bar = 1.71 , s2 = 0.72

sp^2 = ( s1^2 +s2^2 )/2 = 0.5(2.2^2+0.72^2) = 2.6792

sp = sqrt(2.6792) = 1.6368

Test statistic = (4.2-1.71)/ (1.6368*sqrt(2/22))

= 5.04

t-critical = t 0.025 with n1+ n2 -2 = 42 df = 2.018

since TS > t-critical ,we reject the null hypothesis and conclude that there is enough evidence that  there is a difference between the treatment group and placebo group.

b) COnfidence interval

((4.2-1.71) - 2.018*(1.6368*sqrt(2/22)) , (4.2-1.71) + 2.018*(1.6368*sqrt(2/22)) )

(1.49,3.4859)

since 0 is not in confidence interval , hence the results support the common belief that drinking alcohol is hazardous for drivers, pilots, ship captains

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