A consultant wishes to know whether the proportion of innovativ

e executives depends

on whether the executives have a graduate diploma in business a

dministration

(GDBA), a master's degree in business administration (MBA), or

do not hold any of

these degrees in business administration (NODBA). He selects a

random sample from

each of the three populations of executives and analyses the pe

rformance of every

selected executive. On the basis

of these analyses, the consult

ant categorizes each

executive as innovative or not innovative. The results are as f

ollows.

Degree in Business Administration?

Innovative?

NODBA GDBA

MBA

Yes

105

120

35

No

145

50

10

(a) There are two variables in this study, the performance of t

he executives

(innovative or not) and whether an executive has a graduate dip

loma in business

administration, a master's degree in business administration, o

r none. What type

of variables are they and what are their levels of measurement?

Explain your

answers.

(b) Assuming that these data had been generated by a proper mul

tinomial

experiment, which test can the consultant use to see whether th

e three

populations of executives categorized by their qualifications d

iffer with respect to

the proportion of innovative exec

utives? Explain your choice.

(c) Perform the test you chose in part (b) manually at the 5% s

ignificance level. State

the hypotheses, the decision rule, calculate the test statistic

showing the details of

your calculations, make a statistical decision with reference t

o the proper critical

value and draw your conclusion. Based on the relevant critical

value table, what

can you tell about the

p

-value of your test?