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Did I do this problem correctly? A person wants to know whether earning a degree can help improve an individual's income in his county. He

Did I do this problem correctly?

A person wants to know whether earning a degree can help improve an individual's income in his county. He conducts a survey and obtains the following result:

Education attainment Annual income
Below 30,000 30,001-50,000 50,001-70,000 Above 70,000
No degree 29 26 19 5
Associate's 35 39 36 10
Bachelor's 45 50 55 10
Master's 5 15 21 8
PhD or Professional 3 6 9 9

Use SPSS to dothe following:

  1. Show the observed frequencies and expected frequencies.
  2. At = 0.1 level of significance, determine whether there is evidence of a relationship between education attainment and income.

Income * Education Crosstabulation

Education

Total

No Degree

Associate's

Bachelor's

Master's

PhD or Professional

Income

Below 30,000

Count

29

35

45

5

3

117

Expected Count

21.2

32.3

43.0

13.2

7.3

117.0

30,001-50,000

Count

26

39

50

15

6

136

Expected Count

24.7

37.5

50.0

15.3

8.4

136.0

50,001-70,000

Count

19

36

55

21

9

140

Expected Count

25.4

38.6

51.5

15.8

8.7

140.0

Above 70,000

Count

5

10

10

8

9

42

Expected Count

7.6

11.6

15.4

4.7

2.6

42.0

Total

Count

79

120

160

49

27

435

Expected Count

79.0

120.0

160.0

49.0

27.0

435.0

Chi-Square Tests

Value

df

Asymptotic Significance (2-sided)

Pearson Chi-Square

36.332a

12

<.001

Likelihood Ratio

32.271

12

.001

N of Valid Cases

435

a. 2 cells (10.0%) have expected count less than 5. The minimum expected count is 2.61.

P-value = Asymp. Sig. = 0.001 < (0.1). Therefore, there is evidence of a relationship between education and annual income.

Note: The Pearson Chi-Square value of 36.332a is the -statistic as discussed.

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