Question

The null and alternate hypotheses are: H0: μ1 ≤ μ2 H1: μ1 > μ2 A random sample of 24 items from the first population showed a mean of 113 and a standard deviation of 13. A sample of 18 items for the second population showed a mean of 103 and a standard deviation of 14. Use the 0.05 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 0.050 significance level. (Round your answer to 3 decimal places.)

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

d. What is your decision regarding the null hypothesis? Use the 0.05 significance level.

Answer 1

Given that,

For population 1 : n1 = 24, x1-bar = 113 and s1 = 13

For population 2 : n2 = 18, x2-bar = 103 and s2 = 14

The null and alternative hypotheses are,

H0 : μ1 ≤ μ2

H1 : μ1 > μ2

Using TI-83 plus calculator we get,

a) The degrees of freedom for unequal variance test is,

DF = 35

b) t-critical value at significance level of 0.050 with 35 degrees of freedom is, tcrit = 1.690

Decision Rule : Reject H0, if t > 1.690

c) Test statistic = t = 2.362

d) Since, test statistic = 2.362 > 1.690, we reject the null hypothesis.