An experiment was conducted to test the effects of alcohol. Errors were recorded

Question

An experiment was conducted to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for treatment group who drank ethanol and a placebo group. Construct a 95% confidence interval of the difference between the two population means. Do not assume the population standard deviations are equal. Do the results support the belief that drinking is hazardous for drivers, pilots and captains?

x

Find the 95% confidence interval? ____< U1 - U2 <____

x

Explanation / Answer

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=3.19
Standard deviation( sd1 )=2.42
Sample Size(n1)=23
Mean(x2)=1.85
Standard deviation( sd2 )=0.61
Sample Size(n1)=23
CI = [ ( 3.19-1.85) ±t a/2 * Sqrt( 5.8564/23+0.3721/23)]
= [ (1.34) ± t a/2 * Sqrt( 0.27) ]
= [ (1.34) ± 2.074 * Sqrt( 0.27) ]
= [0.26 , 2.42]

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