1. Given the following data from two independent samples from which the population standard deviation is known, conduct a two-tailed hypothesis test to determine if the first sample mean is smaller than the second sample mean, given a 0.01 level of significance.
n1 = 42 n2 = 30
xbar1= 39 xbar2 = 25
sigma1=8 sigma2 = 6
Conduct a two-tailed hypothesis test given the information below.
2. Assuming that the population standard deviations are unknown, but equal for male and female Grade Point Averages (GPAs), use the following sample data to test whether the averages are different at the 0.05 level of significance.
Male GPA's Female GPA's
Sample Size 12 13
Sample Mean 2.8 4.95
Sample Standard Deviation .25 .8
This solution is comprised of a detailed explanation of the various aspects of Hypothesis Test as it pertains to the given problems and provides students with a clear perspective of the calculations and underlying concepts.