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Question A.5 [5] Consider the job satisfaction variable in the study discussed in Question A.3 with its categories "Dissatisfied" and "A Little Satisfied" combined into a category of "Not Satisfied", and the categories "Moderately Satisfied" and "Very Satisfied" into a category of "Satisfied". Further combine the categories "25K" into a category of ">15K". Table A.3 is then simplified into Table A.5. Table A.5 job satisfaction (Y) gender (X) income (Z in $) Not Satisfied Satisfied total Female 15K 33 42 IA VIA 15K 19 22 Male 15K 9 14 15K 25 27 total 86 105 . QA.5(i) Use Table A.5 to answer the following questions: (i.1) Give the sample odds ratio (OR) of job "Not Satisfied" for female vs male, regardless of income. (i.2) Give the two sample ORs of job "Not Satisfied" for female vs male in the two income strata. (i.3) Indicate an interesting phenomenon you observe from (i.1) and (i.2), and then provide your explanation of it. . QA.5(ii) The Fisher's exact test with a 2 x 2 table is one of the statistical methods that do not require a large sample of data and are applicable in the situations similar to this example. Below is the R outputs of the Fisher's exact test with Table A.5 on the independence between job satisfaction (Y) and income (Z) for females. Report the analysis outcome, and comment on limitations of statistical inference with a small sample based on this example. > fisher . test (rbind (c (9,33) , c (3 , 19) ) ) #########females Fisher's Exact Test for Count Data data : rbind (c (9 , 33) , c(3, 19) ) p-value = 0. 5208 alternative hypothesis : true odds ratio is not equal to 1 95 percent confidence interval : 0 . 3664364 11 . 0362226 sample estimates : odds ratio 1 . 713414