Question

In: Statistics and Probability

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to...

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?

Solutions

Expert Solution

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.

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 5.253

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.


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