SCENARIO 12-1
a Corporation Randomly Selects 150 Salespeople and Finds $\pi$

question 28

Multiple Choice

SCENARIO 12-1
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 12-1, what is the critical value when performing a chi-square test on whether the population proportions are different if $\alpha$ = 0.05?

• A)\(\pm\) 1.645
• B)\(\pm\) 1.96
• C)3.841
• D)2.706

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Definitions:

Hypothesis Test

A statistical method that uses sample data to evaluate a hypothesis about a population parameter, determining whether there is enough evidence to reject the null hypothesis.

Rejection Region

In hypothesis testing, the range of values for which the null hypothesis is considered unlikely and is therefore rejected.

Chi-Square Distribution

A statistical distribution that is used to determine the goodness of fit of an observed distribution to an expected one under the null hypothesis.

Critical Value(s)

Specific point(s) on a distribution curve that define the threshold for rejecting the null hypothesis in hypothesis testing.