A Two-Sample $z$ -Test for Two Population Proportions Is to Be Performed Using

question 5

Multiple Choice

A two-sample $z$ -test for two population proportions is to be performed using the $P$ -value approach. The null hypothesis is $H _ { 0 } : p _ { 1 } = p _ { 2 }$ and the alternative is $H _ { A } : p _ { 1 } \neq p _ { 2 }$ . Use the given sample data to find the $p$ -value for the hypothesis test. Give an interpretation of the $p$ -value.
$$n _ { 1 } = 50 , x _ { 1 } = 20 , n _ { 2 } = 75 , \text { and } x _ { 2 } = 15$$

• A) \(P\)-value \(= 0.0032\); If there is no difference in the proportions, there is about a \(0.32 \%\) chance of seeing the observed difference or larger by natural sampling variation.
• B) \(P\)-value \(= 0.0147\); If there is no difference in the proportions, there is about a \(1.47 \%\) chance of seeing the observed difference or larger by natural sampling variation.
• C) \(P\)-value \(= 0.0292\); If there is no difference in the proportions, there is a \(2.92 \%\) chance of seeing the exact observed difference by natural sampling variation.
• D) \(P\)-value \(= 0.0032\); There is about a \(0.32 \%\) chance that the two proportions are equal.
• E) \(P\)-value \(= 0.0147\); There is about a \(1.47 \%\) chance that the two proportions are equal.

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Definitions:

Organic Chemistry

A branch of chemistry that studies the structure, properties, composition, reactions, and preparation of carbon-containing compounds, which include not only hydrocarbons but also compounds with any number of other elements, including hydrogen, nitrogen, oxygen, halogens, phosphorus, silicon, and sulfur.

Reaction

A method whereby one or more materials (known as reactants) are transformed into one or more distinct materials (referred to as products).

Major Product

The product of a chemical reaction that is formed in the greatest amount, differentiated by its higher yield in contrast to minor products.

Stepwise Mechanism

A reaction mechanism that occurs through a series of discrete intermediates and transition states, rather than in a single concerted step.