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:

$3.5	$5.1	$5.2	$3.6	$5	$3.4	$5.3	$6.5	$4.8	$6.3
5.8	4.5	6.3	4.9	4.2

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

$4.1	$2.5	$1.2	$3.5	$5.1	$2.3	$6.1	$1.2	$1.5	$1.3
1.8	2.1

  

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

Degrees of freedom

2.	State the decision rule for 0.05 significance level: H0: μLC ≤ μCK; H1: μLC > μCK. (Round your answer to 3 decimal places.)

Reject H0 if t>

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

Value of the test statistic

4.	Is it reasonable to conclude that Claiborne models earn more? Use the 0.05 significance level.

  (Click to select)RejectFail to reject H₀. It is (Click to select)reasonablenot reasonable to conclude that Claiborne models earn more.

Answer 1

For Claiborne model

= 4.96, s1 = 1.0034, n1 = 15

For Klein model

= 2.725, s2 = 1.6288, n2 = 12

1) df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((1.0034)^2/15 + (1.6288)^2/12)^2/(((1.0034)^2/15)^2/14 + ((1.6288)^2/12)^2/11)

= 17

2) At alpha = 0.05, the critical value is t^* = 1.740

Reject H₀, if t > 1.740

3) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (4.96 - 2.725)/sqrt((1.0034)^2/15 + (1.6288)^2/12)

= 4.163

4) Since the test statistic value is greater than the critical value(4.163 > 1.740), so we should reject H₀.

Reject H₀. It is reasonable to conclude that Claiborne models earn more .