Question

Random samples of female and male UVA undergraduates are asked to estimate the number of alcoholic drinks that each consumes on a typical weekend. The data is below:

Females (Population 1): 0, 1, 1, 0, 2, 2, 1, 0, 4, 1

Males (Population 2): 5, 4, 6, 5, 6, 6, 5, 4, 4, 6

Give a 93.2% confidence interval for the difference between mean female and male drink consumption. (Assume that the population variances are equal.)

Confidence Interval =

Answer 1

Based on the information provided, we assume that the population variances are equal, so then the number of degrees of freedom are  df = n₁ + n₂ - 2 = 10 + 10 - 2 = 18

The critical value for α=0.068 and df = 18 degrees of freedom is t_critical = t^* = 1.942.

The corresponding confidence interval is computed as shown below:

Since the population variances are assumed to be equal, we need to compute the pooled standard deviation, as follows: