Question

The null and alternate hypotheses are:

H₀: ?₁ ? ?₂

H₁: ?₁ > ?₂

A random sample of 24 items from the first population showed a mean of 114 and a standard deviation of 16. A sample of 16 items for the second population showed a mean of 108 and a standard deviation of 12. 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. (is rejected or cannot be rejected)

Answer 1

The null and alternate hypotheses are:

H0: ?1 ? ?2

H1: ?1 > ?2

a)  the degrees of freedom for unequal variance test = 15

Degree of freedom is smaller between n1-1 or n2-1

Degree of freedom =16-1=15

b) decision rule for 0.050 significance level.

Reject H0 if t calculated >1.753

t critical value by using t table.

c) the value of the test statistic

=1.353

d) P value is 0.098 > 0.05 ..............................................by using TDIST(1.353,15,1)

We fail to reject H0.

i.e. cannot be rejected