2. For the following problems, find the expected frequencies of each cell in the
ID: 3225132 • Letter: 2
Question
2. For the following problems, find the expected frequencies of each cell in the table, perform a chi-square test for independence, and comment on the relationship between the variables. Assume the variables are independent.
a. The contingency table shows the results of a random sample of college professors and the years of teaching at the university level.
b. The contingency table shows the results of a random sample of individuals by gender and gas mileage of vehicle owned.
4-7 8-15 lover 15 GenderExplanation / Answer
Part-a
From following results we have enough to rejeect the independence as2(4)=84.58, p=1.86E-17=0.000<0.05. Hence we conclude that gender and and the years of teaching at the university level. are not independent.
Part-b
From following results we have enough to rejeect the independence as2(4)=103.56 p=1.71E-21=0.000<0.05. Hence we conclude that gender and and gas mileage of vehicle owned.. are not independent.
Chi-Square Test Observed Frequencies Teaching Calculations Gender <1 years 1-3 years 4-7 years 8-15 years Over 15 years Total fo-fe Male 35 47 58 135 150 425 -10.3333 -12.2424 -37.8182 15.48485 44.90909 Female 53 68 128 97 54 400 10.33333 12.24242 37.81818 -15.4848 -44.9091 Total 88 115 186 232 204 825 Expected Frequencies Teaching Gender <1 years 1-3 years 4-7 years 8-15 years Over 15 years Total (fo-fe)^2/fe Male 45.33333 59.24242 95.81818 119.5152 105.0909 425 2.355392 2.529892 14.92634 2.006277 19.19126 Female 42.66667 55.75758 90.18182 112.4848 98.90909 400 2.502604 2.688011 15.85924 2.13167 20.39071 Total 88 115 186 232 204 825 Data Level of Significance 0.05 Number of Rows 2 Number of Columns 5 Degrees of Freedom 4 Results Critical Value 9.487729 Chi-Square Test Statistic 84.58139 p-Value 1.86E-17 Reject the null hypothesis Expected frequency assumption is met.Related Questions
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