Construct the Indicated Confidence Interval for the Difference Between Population $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$

question 30

Multiple Choice

Construct the indicated confidence interval for the difference between population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$ Assume that the samples are independent and that they have been randomly selected.
- $\mathrm { x } _ { 1 } = 37 , \mathrm { n } _ { 1 } = 74$ and $\mathrm { x } _ { 2 } = 50 , \mathrm { n } _ { 2 } = 87 ;$ Construct a $95 \%$ confidence interval for the difference between population proportions $\mathrm { p } _ { 1 } - \mathrm { P } _ { 2 }$ .

• A) \(0.317 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.683\)
• B) \(- 0.258 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.683\)
• C) \(- 0.229 < p _ { 1 } - p _ { 2 } < 0.079\)
• D) \(0.346 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.654\)

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Definitions:

Entry Barriers

Obstacles that make it difficult for new competitors to enter a market, including high startup costs, strict regulations, and established brand loyalty.

Competitive Price-searcher Market

A market structure where firms have some control over the pricing of their products because their products are differentiated, but there is intense competition due to low entry barriers.

Economic Profit

The total revenue of a business minus both explicit and implicit costs.

Long-run Equilibrium

A state in which all firms in a market are making normal profits, with no incentive for entry or exit, indicating a stable market condition.