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

question 3

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:

Research Hypotheses

Statements made for a study that predicts a relationship between variables, to be tested through research.

Sampling Error

The discrepancy between a sample statistic and its corresponding population parameter, arising purely by chance because the sample is not a perfect representation of the population.

Nondirectional Research Hypothesis

A hypothesis suggesting a correlation between variables without defining the nature of their interaction.

Generalizability

The extent to which the findings from a study can be applied to a wider population or different contexts.