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Random samples of two freshmen, two sophomores, two juniors, and two seniors from each of four...

Random samples of two freshmen, two sophomores, two juniors, and two seniors from each of four dormitories were asked to rate, on a scale of 1 (poor) to 10 (excellent), the quality of the dormitory environment for studying. The vice-provost for student has asked you to test the null hypothesis that the population mean ratings are the same for the four dormitories and the null hypothesis that the population mean ratings are the same for the four student years. Select the appropriate experimental design for this analysis.

One-Way ANOVA

Two-Way ANOVA

Randomized Block Design

Math   Statistics-And-Probability   
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Answer #1

it is not a one way ANOVA because we have two independent variables, one is year and second is rating of dormitories. we know that one way ANOVA can never be used for two independent variables.

It is not a random block design because the population is not divided into sub-population groups. So, it is not matching the requirement for a random block design

it is a two way ANOVA experimental design because there are two independent variable with multiple levels and we know that the two way ANOVA is good to go when we have two have independent variables.

therefore, option B is correct answer (Two way ANOVA)

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