Suppose the Proportion of Sophomores at a Particular College Who $p _ { s }$

question 9

Multiple Choice

Suppose the proportion of sophomores at a particular college who purchased used textbooks in the past year is $p _ { s }$ and the proportion of freshmen at the college who purchased used textbooks in the past year is $p _ { f }$ . A study found a $90 \%$ confidence interval for $p _ { s } - p _ { f }$ is $( 0.234,0.421 )$ . Give an interpretation of this confidence interval.

• A) We are \(90 \%\) confident that at this college the proportion of sophomores who bought used textbooks is between \(23.4 \%\) and \(42.1 \%\) higher than the proportion of freshmen who bought used textbooks.
• B) We are \(90 \%\) confident that at this college the proportion of freshmen who bought used textbooks is between \(23.4 \%\) and \(42.1 \%\) higher than the proportion of sophomores who bought used textbooks.
• C) We are \(90 \%\) confident that sophomores at this college bought between \(23.4 \%\) and \(42.1 \%\) more used textbooks than freshmen.
• D) We know that \(90 \%\) of all random samples done on the population will show that the proportion of sophomores who bought used textbooks is between \(23.4 \%\) and \(42.1 \%\) higher than the proportion of freshmen who bought used textbooks.
• E) We know that \(90 \%\) of sophomores bought between \(23.4 \%\) and \(42.1 \%\) more used textbooks than freshmen at this college.

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Definitions:

Lowering Price

A strategic move where a seller reduces the price of goods or services to attract more customers or beat competitors.

Monopolist

A market participant that is the sole seller of a good or service, thereby controlling the market.

Nondiscriminating Monopolist

A monopolist who charges the same price to all consumers regardless of their individual demand or willingness to pay.

Marginal Revenue

The supplementary income earned from the sale of one extra unit of a good or service.