A newspaper story headline reads “Gender Plays Part in Monkeys’ Toy Choices, Research Finds—Like Humans, Male Monkeys Choose Balls and Cars, While Females Prefer Dolls and Pots” (Knight Ridder Newspapers, December 8, 2005). The article goes on to summarize findings published in the paper “Sex Differences in Response to Children’s Toys in Nonhuman Primates” (Evolution and Human Behavior [2002]: 467– 479). Forty-four male monkeys and 44 female monkeys were each given a variety of toys, and the time spent playing with each toy was recorded. The table at the top of this page gives means and standard deviations (approximate values read from graphs in the paper) for the percentage of the time that a monkey spent playing with a particular toy. Assume that it is reasonable to regard these two samples of 44 monkeys as representative of the populations of male monkeys and female monkeys. Use a .05 significance level for any hypothesis tests that you carry out when answering the various parts of this exercise.
a. The police car was considered a “masculine toy.” Do these data provide convincing evidence that the mean percentage of the time spent playing with the police car is greater for male monkeys than for female monkeys?
b. The doll was considered a “feminine toy.” Do these data provide convincing evidence that the mean percentage of the time spent playing with the doll is greater for female monkeys than for male monkeys?
c. The furry dog was considered a “neutral toy.” Do these data provide convincing evidence that the mean percentage of the time spent playing with the furry dog is not the same for male and female monkeys?
d. Based on the conclusions from the hypothesis tests of Parts (a)– (c), is the quoted newspaper story headline a reasonable summary of the findings? Explain.
e. Explain why it would be inappropriate to use the two-sample t test to decide if there was evidence that the mean percentage of the time spent playing with the police car and the mean percentage of the time spent playing with the doll is not the same for female monkeys.