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. The following is the amount ($000) earned per month by a sample of 15 Claiborne models:

$3.9	$4.2	$5.1	$5.9	$6.4	$6.6	$6.4	$5.5	$3.8	$4.5
4.5	6.9	3.7	5.0	6.7

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

$4.6	$4.2	$5.2	$5.1	$4.8	$3.9	$4.0	$4.2	$3.6	$3.9
4.3	4.4

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

2. State the decision rule for 0.10 significance level: H₀: μ_Claiborne ≤ μ_{Calvin Klein} ; H₁: μ _Claiborne > μ _{Calvin Klein}. (Round your answer to 3 decimal places.)

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

4. Is it reasonable to conclude that Claiborne models earn more? Use the 3.90 significance level.

Answer 1

Solution: We can use the excel data analysis tool to answer the given questions. The excel output is given below:

t-Test: Two-Sample Assuming Unequal Variances
	Claiborne	Klien
Mean	5.273333333	4.35
Variance	1.314952381	0.244545455
Observations	15	12
Hypothesized Mean Difference	0
df	20
t Stat	2.809064066
P(T<=t) one-tail	0.005418777
t Critical one-tail	1.325340707
P(T<=t) two-tail	0.010837553
t Critical two-tail	1.724718218

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

State the decision rule for 0.10 significance level: H₀: μ_Claiborne≤ μ_{Calvin Klein}; H₁: μ _Claiborne> μ _{Calvin Klein}. (Round your answer to 3 decimal places.)

Reject the null hypothesis, if the test statistic is greater than 1.325

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

Is it reasonable to conclude that Claiborne models earn more? Use the 3.90 significance level.

Yes, it is reasonable to conclude that Claiborne models earn more because the p-value is less than the significance level