Question
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:
- Show the observed frequencies and expected frequencies.
- 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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