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."† The article goes on to summarize findings published in the paper "Sex Differences in Response to Children's Toys in Nonhuman Primates."† 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 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 of female monkeys. Use a 0.05 significance level for any hypothesis tests that you carry out when answering the various parts of this exercise. (Use ????1 for male monkeys and ????2 for female monkeys.)
| Percent of Time | |||||||
|---|---|---|---|---|---|---|---|
| Female Monkeys | Male Monkeys | ||||||
| n | Sample Mean |
Sample Standard Deviation |
n | Sample Mean |
Sample Standard Deviation |
||
| Toy | Police Car | 44 | 9 | 3 | 44 | 17 | 4 |
| Doll | 44 | 21 | 3 | 44 | 10 | 2 | |
| Furry Dog | 44 | 19 | 6 | 44 | 25 | 6 | |
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?
State the appropriate null and alternative hypotheses.
H0: ????1 ? ????2 > 0 Ha: ????1 ? ????2 = 0
H0: ????1 ? ????2 < 0 Ha: ????1 ? ????2 = 0
H0: ????1 ? ????2 < 0 Ha: ????1 ? ????2 > 0
H0: ????1 ? ????2 = 0 Ha: ????1 ? ????2 > 0
H0: ????1 ? ????2 = 0 Ha: ????1 ? ????2 < 0
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)
t=
P-value=
State the conclusion in the problem context.
We reject H0. 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.
We fail to reject H0. These data do not provide convincing evidence that the mean percentage of the time spent playing with the doll is greater for female monkeys than for male monkeys.
We fail to reject H0. 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.
We reject H0. These data do not 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?
State the appropriate null and alternative hypotheses.
H0: ????1 ? ????2 < 0 Ha: ????1 ? ????2 ? 0
H0: ????1 ? ????2 = 0. Ha: ????1 ? ????2 ? 0
H0: ????1 ? ????2 ? 0 Ha: ????1 ? ????2 > 0
H0: ????1 ? ????2 > 0. Ha: ????1 ? ????2 ? 0
H0: ????1 ? ????2 ? 0. Ha: ????1 ? ????2 = 0
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)
t=
P-value=
State the conclusion in the problem context.
We reject H0. These data do not 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.
We reject H0. 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.
We fail to reject H0. These data do not 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
.We fail to reject H0. 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.
No, it is not reasonable because male monkeys show more interest in the "feminine" toy, and female monkeys show more interest in the "masculine" toy.
No, it is not reasonable because both male and female monkeys show similar interest in the "masculine" and "feminine" toys.
Yes, it is reasonable because male monkeys show more interest in the "masculine" toy, female monkeys show more interest in the "feminine" toy, and both show the same interest in the "neutral" toy.
No, it is not reasonable because male monkeys and female monkeys show different interest in the "neutral" toy, so their interest may be due to something other than the gender of the toy.
(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 are not the same for female monkeys.
It is inappropriate because the mean percentage of the time spent playing with the police car and the mean percentage of the time spent playing with the doll come from two independent random samples.
It is inappropriate because the mean percentage of the time spent playing with the police car and the mean percentage of the time spent playing with the doll do not come from two independent random samples.
It is inappropriate because the sample standard deviation for the percentage of the time spent playing with the police car is the same as the sample standard deviation for the percentage of the time spent playing with the doll.
It is inappropriate because the police car is a "masculine" toy and the doll is a "feminine" toy.