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Choose a \(t\) -test for each situation: one-sample \(t\) -test, twosample \(t\) -test, paired \(t\) -test, and no \(t\) -test. a. A random sample of car dealerships is obtained. Then a student walks onto each dealer's lot wearing old clothes and finds out how long it takes (in seconds) for a salesperson to approach the student. Later the student goes onto the same lot dressed very nicely and finds out how long it takes for a salesperson to approach. b. A researcher at a preschool selects a random sample of 4 -year-olds, determines whether they know the alphabet (yes or no), and records gender. c. A researcher calls the office phone for a random sample of faculty at a college late at night, measures the length of the outgoing message, and records gender.

Step by step solution

01

Situation A

In this situation, the times it takes for a salesperson to approach to the same student dressed differently are recorded. These measurements are paired because they come from the same individual across different conditions. Therefore, a Paired t - test can be applied.

02

Situation B

In this situation, a researcher is comparing two categorical variables (knowledge of the alphabet and gender) rather than two means. A t-test is not appropriate for this situation.

03

Situation C

In this situation, there are two independent groups: faculty of different genders. The research is comparing the mean length of their outgoing messages. As the groups are unpaired, a two-sample t-test would be used.

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