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

question 13

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:

Working Capital Investment

The funds invested in the short-term assets of a company, such as inventory and receivables, to support its daily operations.

Salvage Value

The estimated residual value of an asset at the end of its useful life, important for calculating depreciation.

Discount Rate

The interest rate used in discounted cash flow analysis to determine the present value of future cash flows or to evaluate the attractiveness of an investment.

Incremental Cost Approach

A decision-making process that focuses on the changes in total cost resulting from a specific business decision, considering only the relevant costs and benefits that differ between alternatives.