SCENARIO 10-10
a Corporation Randomly Selects 150 Salespeople and Finds $\pi _ { 1 } \text { and } \pi _ { 2 }$

question 177

Short Answer

SCENARIO 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-
improvement course would like such a course. The firm did a similar study 10 years ago in which
60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are
assumed to be independent random samples. Let $\pi _ { 1 } \text { and } \pi _ { 2 }$ represent the true proportion of workers
who would like to attend a self-improvement course in the recent study and the past study,
respectively.
-Referring to Scenario 10-11, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } = 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$
b) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } = 0$
c) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$
d) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$

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Definitions:

Network Theory

A theory in sociology and other fields that examines how networks of social interactions influence behavior and outcomes.

Rational Choice Theory

A theory in social science that posits individuals always make prudent and logical decisions that provide them with the highest amount of personal utility.

Corporate Actors

Entities such as companies or businesses that are capable of making decisions and acting in the economic or social sphere, often with considerable influence.

James Coleman

An influential American sociologist known for his contributions to educational sociology, social theory, and the concept of social capital.