After watching nursery-school children, Ken Garoo wants to test the hypothesis that some toys are more fun to play with than others. He decides to compare “fun” toys (blocks) with “unfun” toys (stuffed animals). He also
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After watching nursery-school children, Ken Garoo wants to test the hypothesis that some toys are more fun to play with than others. He decides to compare “fun” toys (blocks) with “unfun” toys (stuffed animals). He also wishes to see if there is a sex difference, as well, so sex is added as an independent variable. A) What kind of design is needed? B) Diagram it out. C) Assuming 20 subjects are needed per cell, how many subjects are needed for this study?
A) The type of design needed in this study would be a 2x2 factorial design. This type of design is needed because we will be able to test the factors within one sample. Also in this design, we can test all possible combinations between one another. For example, fun toys with males and fun toys with females, or unfun toys with females and unfun toys with males.
B)
Fun toys
Unfun toys Male 20 20 Female 20 20
• Assuming there are 20 subjects needed per cell, there would need to be 80 subjects for this study.
20 + 20 + 20 + 20 = 80
• Bill Board is “lording” his SAT score over his friend, Rhoda Dendron, who took the ACT. “You only got a 25 in math,” he chortled, “while I got a 300 in math.” Given that the SAT has a μ of 500 and a σ of 100, and the ACT has a μ of 20 and a σ of 5, what is wrong with Bill’s logic (give the answer in both z scores and percentile ranks).
Bills logic is wrong because the scoring for the ACT and the scoring for the SAT are completely different and cannot be compared to one another. Here is breakdown in percentile ranks and z scores:
300/800 in SAT Math = 37.5%
25/36 ACT Math = 69%
z=x−μ / standard
deviation Rhoda z:
25-20/5 = 1
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