SCENARIO 10-10
a Corporation Randomly Selects 150 Salespeople and Finds $\pi$

question 145

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 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:

Short-Run Adjustments

Refers to the changes firms make in response to changing market conditions in the short term when at least one production factor is fixed.

Oligopolists

Firms that are part of an oligopoly, a market structure with a small number of firms dominating the market, leading to limited competition.

Inverted-U Theory

A theoretical concept suggesting that a variable's effect on a particular outcome increases to a point but then begins to decrease as the variable continues to increase.

Market Structures

The organizational and other characteristics of a market that significantly affect the nature of competition and pricing within that market.