Salary 2010 ($) 37,000 61,000 35,000 41,000 73,000 34,000 41,000 71,000 65,000 40,000 70,000 21,000 34,000 56,000 53,000 8,000 36,000 71,000 42,000 27,000 Salary 2008 ($) 52,000 44,000 31,000 51,000 55,000 40,000 28,000 55,000 59,000 37,000 61,000 38,000 52,000 49,000 50,000 59,000 55,000 61,000 48,000 46,000 Salary 2010 ($) 52,000 35,000 50,000 64,000 68,000 53,000 61,000 41,000 63,000 48,000 45,000 46,000 29,000 46,000 53,000 16,000 40,000 48,000 52,000 56,000 Salary 2008 ($) 35,000 56,000 53,000 52,000 50,000 46,000 60,000 45,000 50,000 43,000 66,000 52,000 39,000 47,000 39,000 41,000 58,000 42,000 56,000 52,000
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)
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.
(Which one is correct)
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H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0
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H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0
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H0: μ1 − μ2 ≤ 0; HA: 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
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p-value < 0.01
c. At the 5% significance level, have salaries gone down from 2008 to 2010?
(Which one is correct)
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Reject H0; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.
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Reject H0; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.
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Do not reject H0; there is evidence that the starting salary of college graduates has declined from 2008 to 2010.
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Do not reject H0; there is not sufficient evidence that the starting salary of college graduates has declined from 2008 to 2010.
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