Question

The null and alternate hypotheses are: H0:µ1≤µ2. H0:µ1>µ2. A random sample of 29 items from the first population showed a mean of 112 and a standard deviation of 9. A sample of 15 items for the second population showed a mean of 97 and a standard deviation of 12. Use the .01 significance level.

a. Find the degrees of freedom for unequal variance test

b. State the decision rule for .1 significance level

c. Compute the value of the test statistic.

Answer 1

a)

df = 15 - 1 = 14

b)

Rejection Region
This is right tailed test, for α = 0.1 and df = 14
Critical value of t is 1.345.
Hence reject H0 if t > 1.345

c)

t = (x1-x2)/sqrt(s1^2/n1+s2^2/n2)
= (112- 97)/sqrt(9^2/29 + 12^2/15)
= 4.261