Question

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether mu 1μ1greater than>mu 2μ2 at the alphaαequals=0.10 level of significance for the given sample data. ​(b) Construct a 90​% confidence interval about mu μ1−μ2.

Population 1 Population 2

n 23	19
x 46.2	45.1
s 5.1	13.4

Find the test statistic for the hypothesis test

Answer 1

a) We are testing, H0: u1= u2 vs H1: u1>u2

From the sample data, x1 - x2 = 1.1

S^2 = 22*5.1^2 + 18*13.4^2/23+19-2 = 95.1075

So the test statistic is: 1.1/√95.1075*(1/23 + 1/19) = 0.3639

The critical value of this test is at t 23+19-2 ie t40

So at alpha = 0.1 critical value is 1.303

Since our test statistic is less than the critical value, we have insufficient evidence to Reject H0. So we cannot conclude that u1>u2 at the 10% significance level.

b) 90% confidence interval for u1- u2 is given as:

1.1 +- 1.684*√95.1075*√1/23 + 1/19

=(-3.991, 6.191)

The confidence interval also gives us the same answer to the test, since it contains 0, it isn't statistically significant so we cannot Reject H0.