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.

1. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

2. State the decision rule for 0.100 significance level. (Round your answer to 3 decimal places.)

3. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

4. What is your decision regarding the null hypothesis? Use the 0.10 significance level.

Answer 1

a) Calculation for degrees of freedom

= 153.58901

= 6.861479

degrees of freedom= 153.58901 / 6.861479= 22

b) For 0.1 with df = 22 , one tailed critical value of t is

tc = 1.321  ( from t table)

This is a right tailed test ( as alternative hypothesis )

Therefore decision rule is reject H0

if calculated t > 1.321

c) Test statistic

= 4.26

d) Since calculated value of t > 1.321

We reject H0 .

At 0.10 level of significance, there is sufficient evidence to conclude that