Question

Recent evidence suggests that graduating from college during bad economic times can impact the graduate's earning power for a long time (Financial Times, June 1, 2012). An associate dean at a prestigious college wants to determine if the starting salary of his college graduates has declined from 2008 to 2010. He expects the variance of the salaries to be different between these two years. The data are shown in the accompanying table and are contained in the accompanying Excel file. (You may find it useful to reference the appropriate table: z table or t table)

Salary 2008 ($)	Salary 2010 ($)	Salary 2008 ($)	Salary 2010 ($)
38,000	31,000	45,000	45,000
50,000	65,000	43,000	31,000
55,000	31,000	32,000	52,000
54,000	46,000	54,000	66,000
54,000	65,000	53,000	71,000
47,000	33,000	40,000	55,000
62,000	41,000	25,000	60,000
50,000	65,000	56,000	41,000
48,000	68,000	54,000	62,000
41,000	42,000	37,000	46,000
63,000	70,000	61,000	40,000
50,000	22,000	40,000	52,000
35,000	30,000	52,000	28,000
42,000	55,000	52,000	47,000
38,000	57,000	58,000	55,000
41,000	10,000	62,000	21,000
58,000	34,000	48,000	40,000
40,000	64,000	62,000	39,000
53,000	47,000	45,000	58,000
48,000	24,000	44,000	51,000

Click here for the Excel Data File

Let Sample 1 be the sample of the starting salary of college graduates in 2008 and Sample 2 be the sample of the starting salary of college graduates in 2010.

a. Specify the competing hypotheses that determine whether the starting salary of college graduates has declined from 2008 to 2010.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

c. At the 5% significance level, have salaries gone down from 2008 to 2010?

• Reject H₀; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.

• Reject H₀; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.

• Do not reject H₀; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.

• Do not reject H₀; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

a) H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b) p-value > 0.10

c) Do not reject H₀; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.

answered by: anonymous