In the Context of a Hypothesis Test for Two Proportions $\overline { \mathrm { p } }$

question 97

Multiple Choice

In the context of a hypothesis test for two proportions, which of the following statements about the pooled sample proportion, $\overline { \mathrm { p } }$ , is/are true?
I. It estimates the common value of $\mathrm { p } _ { 1 }$ and $\mathrm { p } _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { \mathrm { p } } 1$ and $\hat { \mathrm { p } } 2$ .
III. It is equal to the proportion of successes in both samples combined.

• A) I and III
• B) III only
• C) I, II, and III
• D) I and II

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Definitions:

Sole Proprietorship

A type of enterprise owned and operated by one person, where there is no legal distinction between the owner and the business operation.

Double Taxation

The imposition of two or more taxes on the same income, asset, or financial transaction.

Not-for-Profit Organization

An organization that operates for purposes other than making a profit, often focusing on social, educational, or charitable objectives.

Military Organization

An entity structured to use armed forces for purposes of defense, security, or warfare operations.