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	$5	$3.4	$3.5	$5.6	$5.7	$6.8	$6.6	$3	$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

  

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 0.1 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 0.1 significance level.

(Click to select)Fail to rejectReject H0. It is (Click to select)not reasonablereasonable to conclude that Claiborne models earn more.

Answer 1

1)

	sample 1		sample 2
x1                     =	4.813	x2                    =	4.367
s1                     =	1.288	s2                    =	0.591
n1                    =	15.000	n2                    =	12.000

degrees of freedom for unequal variance test =20

2)

for 0.1 level ,rght tail test &20 df, critical t=			1.325
Decision rule:reject Ho if test statistic t>1.325

3)

standard error se=√(S21/n1+S22/n2)=			0.37
test stat t =(x1-x2-Δo)/Se=		1.195

4)

Fail to reject Ho , not reasonable to conclude that Claiborne models earn more.