Among 1,000 managers with degrees in business administration, the following data
ID: 3072710 • Letter: A
Question
Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration.
Major
Top Management
Middle Management
TOTAL
Management
280
220
500
Marketing
120
80
200
Accounting
150
150
300
TOTAL
550
450
1000
1.Determine if the position in management is independent of field (major) of concentration.
2.State the null and alternative hypotheses for a contingency table test if we want to determine if the position in management is independent of field (major) of concentration.
3.State the decision rule for the critical value approach. Let alpha = 0.01.
4.Calculate the expected frequency for the cell “Marketing” and “Middle Management.”
5.If the Chi Square statistic is 5.253 what is your conclusion?
Major
Top Management
Middle Management
TOTAL
Management
280
220
500
Marketing
120
80
200
Accounting
150
150
300
TOTAL
550
450
1000
Explanation / Answer
Ans:
H0:The position in management is independent of field (major) of concentration.
Ha:The position in management is not independent of field (major) of concentration.
Chi square test statistic=5.253
df=(3-1)*(2-1)=2
critical chi square value=CHIINV(0.01,2)=9.210
Decision rule:
Reject H0,if Chi square test statistic>9.210
As,chi square test statistic=5.253 is less than 9.210,we fail to reject the null hypothesis and we can conclude that the position in management is independent of field (major) of concentration.
Observed count(fo) Major Top Management Middle Management TOTAL Management 280 220 500 Marketing 120 80 200 Accounting 150 150 300 TOTAL 550 450 1000 Expected count(fe) Major Top Management Middle Management TOTAL Management 275 225 500 Marketing 110 90 200 Accounting 165 135 300 TOTAL 550 450 1000 Chi square=(fo-fe)^2/fe Major Top Management Middle Management TOTAL Management 0.091 0.111 0.202 Marketing 0.909 1.111 2.020 Accounting 1.364 1.667 3.030 TOTAL 2.364 2.889 5.253Related Questions
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