Question

Consider the following data for two independent random samples taken from two normal populations with equal variances. Find the 95% confidence interval for µ1 - µ2. Sample 1: 11,5,12,9,6,8 Sample 2: 12,9,16,13,11,11

What are the left adn right endpoints?

Answer 1

= 8.5, s1 = 2.7386, n1 = 6

= 12, s1 = 2.3664, n2 = 6

DF = 6 + 6 - 2 = 10

At 95% confidenceinterval the critical value is t_{0.025, 10} = 2.228

The pooled variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                        = (5 * (2.7386)^2 + 5 * (2.3664)^2)/(6 + 6 - 2)

                                        = 6.55

The 95% confidence interval is

+/- t_{0.025, 10} * sqrt(s_p²/n1 + s_p²/n2)

= (8.5 - 12) +/- 2.228 * sqrt(6.55/6 + 6.55/6)

= -3.5 +/- 3.292

= -6.792, -0.208

Left endpoint = -6.792

Right endpoint = -0.208