Question

Recent evldence suggests that graduating from college during bad economic times can impact the graduate's earning power fora long time (Financlai Times, June 1, 2012). An assoclate dean at a prestiglous 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 ttable) Salary 2008 Salary 2010 Salary 200B Salary 2010 34,000 36,000 45,000 46, 000 70,000 36,000 3B, 000 56,000 49, 000 42,000 65,000 36,000 29, 000 50,000 41,000 49,000 53,000 47,000 24, 000 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

Answer 1

Using excel,

Assuming that the salary of the same college graduates are measured in 2008 and 2010 ( i.e. assuming the observations are paired), we may run a paired t test.

a. Let $\dpi{80} \mu _{1},\mu _{2}$ denote the mean salary of the college graduates in the year 2008 and 2010 respectively.We have to test whether the starting salary has declined from 2008 to 2010.

To test:$\dpi{80} H_{0}:\mu _{1}\geq \mu _{2}$   Vs $\dpi{80} H_{a}:\mu _{1}<\mu _{2}\Rightarrow H_{a}:\mu _{1}-\mu _{2}<0$ ............(One tailed test)

(The null is always the negation of the claim to be tested.)

Running a paired t test,

HomeInsert Page Layout Formulas Data ReviewView e- connections 화 2 3 Y,Rle pply 물 E 3 睜盼相相 Hide Detail |&Data Analysis Show Detail Properties From From From From Other Existing Retresh Access WebText Sources 차 sort Filter Advanced || Columns Duplicates validation Text to Remove ta Consolidate What-It Group Ungroup Subtotal Connections All-Edit Links Analysis Get External Dat Connections Sort & Filter Data Tools Outline Analysis F4 1 Salary 2008 Salary 2010 37000 51000 55000 52000 45000 46000 59000 48000 49000 2000 12 68000 32000 Data Analysis Analysis Tools Hstogram Moving Average Random Number Generaton Rank and Percentie 41000 36000 42000 65000 42000 t-Test:Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances z-Test: Two Sample for Means 21000 36000 5 0

B1 t-Test: Paired Two Sample for Means 1 Salary 2008 Salary 2010 OK 32000 64000 34000 41000 70000 36000 42000 72000 65000 42000 73000 21000 29000 50000 37000 51000 Variable 1 Range: Variable 2 Range: Hypothesized Mean Difference: SA$1:SA$41 $B$1:$B$41 4 52000 46000 59000 48000 49000 42000 Labels Alpha: 0.05 Output options Output Range: ONew Worksheet Ply: O New Workbook 10 12 13 14 15 50000 36000 45000 1000

We get the output:

1 Salary 2008 Salary 2010 32000 t-Test: Paired Two Sample for Means 37000 Salary 2008 Salary 2010 46775 68804487.18 262435256 51000 4 Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<-t one-tail t Critical one-tail P(T<t two-tail t Critical two-tail 48375 52000 41000 0.104 0 39 0.534 0.298 1.685 0.596 2.023 36000 59000 42000 10 49000 42000 42000 12 13 14 15 16 21000 36000 41000 52000

b. The p-value expresses the probability of obtaining a result that is as extreme as obtained in the sample, when the null hypothesis is true. From the output, the p-value of the test p = 0.298 > 0.05

c. Since, the p-value of the test p = 0.298 > 0.05, the test result is not significant.We fail to reject H₀ at 5% level; there is not sufficient evidence that the average starting salary of college graduates has declined from 2008 to 2010.