Question

College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 300 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Table 11.40 shows the data. Conduct a test of independence.

Major	< $50,000	$50,000-$68,999	$69,000+
English	5	20	5
Engineering	10	30	60
Nursing	10	15	15
Business	10	20	30
Psychology	20	30	20

Table 11.40

Answer 1

Answer:

The null hypothesis is shown below: H:The starting salaries after graduation are independent of the majors of students.

Against the alternative hypothesis as shown below: H: The starting salaries after graduation are dependent of the majors of students.

The degrees of freedom can be calculated by the formula given below: df = (number of columns - 1)(number of rows -1) Therefore, df =(number of columns - 1)(number of rows - 1) = (3-1)(5-1) = 2x4

d. From above calculation, it is clear that the distribution for the test is

The observed value table is already given in the textbook. Calculate the expected frequencies by using the formula shown below: (row total)(column total) overall total All calculations can be done in excel worksheet. Hence, the expected (E) values table is shown below: E29 A O f =SUM(B29:D29) B C Observed frequency table D E S50000 Total 30 50000-S68999 S69000 20 60 15 10 30 Major English 5 Engineering 6 Nursing 7 Business Psychology Total 100 10 20 40 60 10 20 230 30 115 130 300 Expected frequency table 12 Major English 15 Engineering 16 Nursing 17 Business 18 Psychology <S50000 5.5 18.33333333 7.333333333 50000-S68999 S69000 11.5 13 38.33333333 43.33333 15.33333333 17.33333 23 26 88.16666667 99.66667 11 42.16666667

The test statistic of independence test is given below: Test statistic = 5 (0-E)" E To calculate (0-E) apply formula = ((B4-B14))/B14in cell B24 and drag the same E formula up to cell D28. After that, take total of columns total and rows total. The table of test statistic is shown below: E29 fx =SUM(B29:029) | Ε Test statistic Major English 25 Engineering 26 Nursing 27 Business 28 Psychology Total <$50000 0.045454545 3.787878788 0.96969697 0.090909091 11.65283267 16.54677207 S50000-S68999 S69000 Total 6.282608696 4.923077 11.25114016 1.811594203 6.410256 12.0097294 0.007246377 0.314103 1.291045911 0.391304348 0.615385 1.097598054 38.37460618 63.68004 25.64951353 46.8673598 75.94287 | 139.356997 Hence, the test statistic is 139.4

The p-value can be calculated in excel by using CHIDIST(formula as shown below: D E 30 A 1 fac =CHIDIST(E29,8) B C Test statistic D E 23 Major 24 English 25 Engineering 26 Nursing 27 Business 28 Psychology 29 Total <$50000 0.045454545 3.787878788 0.96969697 0.090909091 11.65283267 16.54677207 50000-S68999 S69000 T otal 6.282608696 4.923077 11.25114016 1.811594203 6.410256 12.0097294 0.007246377 0.314103 1.291045911 0.391304348 0.615385 1.097598054 38.37460618 63.68004 25.64951353 46.8673598 75.94287 139.356997 p-value L 0.00 30 Hence, the p-value is 0.00

The chi-square sketch is shown below: p-value = 0.00 8 139.4

i. Alpha: 0.05 ii: Decision: Reject the null hypothesis H, iii. Reason for decision: Because p-value < a iv. Conclusion: There is sufficient evidence to insure that the starting salaries after graduation are dependent of the majors of students.

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