Question

An experiment to test the effects of alcohol on motor skills was conducted for a group that drank alcohol and a group that had a placebo. The 22 individuals in the alcohol group had a mean error rate of 4.20 and a standard deviation of 2.20. The 22 individuals in the placebo group had a mean error rate of 1.71 and a standard deviation of 0.72.

a. Construct a 95% confidence interval for the difference in the population means.

b. Interpret the interval.

c. Does the data indicate that drinking alcohol affects motor skills? If “YES”, explain why. If “NO”, what does the data indicate about drinking alcohol and motor skills? No credit for “YES/NO” answer only

Answer 1

a)

T-test for two Means Confidence Interval -Unequal Variance

The following information about the sample has been provided: a. Sample Means : Xˉ1​=4.2 and Xˉ2​=1.71 b. Sample Standard deviation: s1=2.2 and s2=0.72 c. Sample size: n1=22 and n2=22 d. Level of confidence is 95% The degrees of freedom Assuming that the population variances are unequal, the degrees of freedom are given by Critical Value Based on the information provided, the significance level is α=0.05, and the degree of freedom is 25.4475. Therefore the critical value is tc​=2.0595. This can be found by either using excel or the t distribution table. Standard Error The Standard error is computed as: Confidence Interval The 95% Confidence interval is computed as:

b)

Therefore, we are 95% confident that the true difference between population means is contained by the interval (1.4736, 3.5064)

c)

YES, the data indicate that drinking alcohol affects motor skills. This is because 0 is not contained in the above confidence interval which is positive. Hence the mean error rate for people who drink alcohol seems to be higher than those who do not (in placebo group)

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