Question

The null and alternate hypotheses are:

H0: μ1 ≤ μ2
H1: 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 0.10 significant level.
a. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)
b) State the decision rule for 0.100 significance level. (Round your answer to 3 decimal places.)
reject H0 if t >
c) Compute the value of the test statistic
d) What is your decision regarding the null hypothesis? Use the 0.10 significance level.

Answer 1

Explanation:

Given that the null and alternate hypotheses are:

H0: μ1 ≤ μ2

H1: μ1 > μ2

Group Group One Group Two

Mean 112.00 97.00

SD 9.00 12.00

SEM 1.67 3.10

N 29 15

The mean of Group One minus Group Two equals 15.00

a) df = 42

standard error of difference = 3.212

b) Reject H0 if t statistic >1.302

t = 4.6699

Since t > 1.302, we reject null hypothesis

It is evident that the mean I is greater than mean 2.