Question

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of 15 Claiborne models:

$4.0	$5.0	$3.4	$3.5	$5.6	$5.7	$6.8	$6.6	$3.0	$4.3
3.9	3.2	5.8	5.1	6.3

The following is the amount ($000) earned by a sample of 12 Klein models.

$3.5	$4.5	$4.1	$4.1	$3.6	$3.8	$4.5	$4.6	$4.8	$5.2
5.4	4.3

A.) Find the degrees of freedom for unequal variance test. (round down to nearest whole #)

B.) State the decision rule for 0.10 significance level. (round to 3 decimal places)

C.) Compute the value of the test statistic. (round to 3 decimal places)

Answer 1

Liz Claiborne:

The sample data, x1 : (4.0, 5.0, 3.4, 3.5, 5.6, 5.7, 6.8, 6.6, 3.0, 4.3, 3.9, 3.2, 5.8, 5.1, 6.3)

The sample size, n1=15

The sample mean:

The sample standard deviation:

Calvin Klein :

The sample data, x2 : (3.5,4.5,4.1,4.1,3.6,3.8,4.5,4.6,4.8,5.2,5.4,4.3)

The sample size, n2=12

The sample mean:

The sample standard deviation:

Now,

We want to test

Null hypothesis:

Ho : μ1 ≤ μ2 i.e. mean amount earned per month by models featuring Liz Claiborne attire is equal to mean amount earned per month by models featuring Calvin Klein.

Alternative hypothesis:

H1 : μ1 μ2  i.e. mean amount earned per month by models featuring Liz Claiborne attire is not equal to mean amount earned per month by models featuring Calvin Klein

A) The degrees of freedom for unequal variance test is given by the formula :

The usual practice is to round down to the integer, so we use 21 degrees of freedom.

B) The decision rule for the 0.1 significance level, at 21 df:

Reject the null if,

(two-sided critical value)

(from t-table)

Decision rule: Reject H0 if tcalculated 1.721

C) The value of the test statistic is given by :

  

  

Since   tcalculated = 1.195 <1.721, hence the null hypothesis is not rejected.