The heights are measured for a simple random sample of 9 female models. The mean
ID: 2960340 • Letter: T
Question
The heights are measured for a simple random sample of 9 female models. The mean height of the models are 69.8 inches and a standard deviation of 1.9 inches. A sample is taken of the heights of 40 women who are not models and with a mean of 61.2 inches and a standard deviation of 2.5 inches. Using a .05 significance level to test the claim that the mean height of female models is greater than the mean height of women who are not models. Assume that the two samples are independent simple random samples selected from normal distributed populations. Do not assume that the population standard deviations are equal.Do you accept or reject the null hypothesis?
Explanation / Answer
Given modes: n1=9, xbar1=69.8, s1=1.9
not models: n2=40, xbar2=61.2, s2=2.5
The test hypothesis is
Ho:1<=2
Ha:1>2
The test statistic is
Z=(xbar1- xbar2)/[s1^2/n1 + s2^2/n2]
=(69.8-61.2)/sqrt(1.9^2/9 + 2.5^2/40)
=11.52
Given a=0.05, the critical value is Z(0.05)=1.645.
Since Z=11.52>1.645, we reject Ho.
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