Question

Independent and Dependent Samples Which of the following involve independent samples?

a. Data Set 14 “Oscar Winner Age” in Appendix B includes pairs of ages of actresses and actors at the times that they won Oscars for Best Actress and Best Actor categories. The pair of ages of the winners is listed for each year, and each pair consists of ages matched according to the year that the Oscars were won.

b. Data Set 15 “Presidents” in Appendix B includes heights of elected presidents along with the heights of their main opponents. The pair of heights is listed for each election.

c. Data Set 26 “Cola Weights and Volumes” in Appendix B includes the volumes of the contents in 36 cans of regular Coke and the volumes of the contents in 36 cans of regular Pepsi.

Short answer

a. It is a dependent sample.

b. It is a dependent sample.

c. It is an independent sample.

Step-by-step solution

Define independent and dependent samples

Independent samples were taken from two populations. The values are not associated with one other.

Dependent samples have a relationship between values such that each value of one sample is related to another value of another sample.

Identify the samples

a. Any pair of actors and actress is related by the year in which they won the Oscars. Hence, each pair consists of ages matched according to the year or time. Thus, the samples are dependent.

b. Any pair of presidents and opponents recorded for height are related by the year of election. Thus, the samples are dependent.

c. The two samples for contents of 36 cans in each group, Pepsi and Cokeare not related to each other. Thus, the samplesare independent.

Only part (c) describes independent samples.