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): 2, 2, 0, 3, 0, 2, 1, 0, 4, 4 Males (Population 2): 5, 5, 8, 7, 8, 9, 6, 7, 5, 6 Give a 94.5% confidence interval for the difference between mean female and male drink consumption. (Assume that the population variances are equal.) Confidence Interval =

Answer 1

For females

= 1.8, s1 = 1.55, n1 = 10

For males

= 6.6, s2 = 1.43, n2 = 10

The pooled variance (s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2) = (9 * (1.55)^2 + 9 * (1.43)^2)/(10 + 10 - 2) = 2.2237

df = 10 + 10 - 2 = 18

At 94.5% confidence interval the critical value is t^* = 2.052

The 94.5% confidence interval is

+/- t^* * sqrt(s_p²/n1 + s_p²/n2)

= (1.8 - 6.6) +/- 2.052 * sqrt(2.2237/10 + 2.2237/10)

= -4.8 +/- 1.3685

= -6.1685, -3.4315