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 (Population LC) with those of Calvin Klein (Population CK). Assume the (unknown) population standard deviations are not equal. The following is the amount ($000) earned per month by a sample of Claiborne models:

$5.4	$4.3	$3.7	$6.7	$4.9	$5.9	$3.1	$5.2	$4.7	$3.5
5.8	4	3.1	5.6	6.9

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

$2.5	$2.6	$3.5	$3.4	$2.8	$3.1	$4	$2.5	$2	$2.9
2.7	2.3

(1)	Find the degrees of freedom for unequal variance test. (Carry at least 3 decimals in your intermediate calculations. Round down your answer to the next lower whole number.)

Degrees of freedom

(2)	State the decision rule for 0.01 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. (Carry at least 3 decimals in your intermediate calculations. 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 0.01 significance level.

  (Fail to reject or Reject) H₀. It is (not reasonable or reasonable) to conclude that Claiborne models earn more.

Answer 1

using excel>data>data analysis>t test for unequal variance

we have

t-Test: Two-Sample Assuming Unequal Variances
	Claiborne models	Klein models
Mean	4.853333	2.858333
Variance	1.495524	0.315379
Observations	15	12
Hypothesized Mean Difference	0
df	21
t Stat	5.620652
P(T<=t) one-tail	7.03E-06
t Critical one-tail	2.517648
P(T<=t) two-tail	1.41E-05
t Critical two-tail	2.83136

Ans 1 )

Degrees of freedom

21

2 )

Reject H0 if t>

2.518

3 )

Value of the test statistic

5.621

4 )

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