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.
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
H_{0}: μ_{1} − μ_{2} ≥ 0; H_{A}: μ_{1} − μ_{2} < 0
H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
b. Find the p-value.
p-value < 0.01
c. At the 5% significance level, have salaries gone down from 2008 to 2010?
Reject H_{0}; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.
Reject H_{0}; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.
Do not reject H_{0}; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.
Do not reject H_{0}; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.
The statistical software output for this problem is:
On the basis of above output:
a) H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
b) p-value > 0.10
c) Do not reject H_{0}; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.
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