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."t 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 u, for male monkeys and u, for female monkeys.) Percent of Time Female Monkeys Male Monkeys Sample Mean Sample Standard Sample Mean Sample Standard Deviation n Deviation Police Car 44 44 17 4 Тoy Doll 44 21 44 8 Furry Dog 44 19 44 26 n USE SALT "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 (a) The police car was considered than for female monkeys? State the appropriate null and alternative hypotheses. O Ho: H1 - 42 > 0 Hi H1 - H2 = 0 O Ho: H1 - 42 0 O Hoi Hq- Hz = 0 H,: H1 - H2 > 0 O Ho: H1 - 42 = 0 H: H, - H, < 0

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...