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1) For a population that has a standard deviation of 20, figure the standard devation of the distribution of sample means for samples of size: (a) 2 X (b) 3 X (c) 4 X (d) 9 X n n n n 20 14.14 2 20 11.55 3 20 10.0 4 20 6.67 9 2) For each of the following samples that were given an experimental treatment, test whether they are different from the general population: The general population of individuals has a mean of 40, a standard deviation of 6, and follows a normal distribution. Carry out the full five steps of hypothesi testing with a two tailed test at the alpha level of 0.05. (a) a sample of 1 with a mean of 44 H0: The sample has the same mean as the population: = 40 HA: The sample has a different mean as the population: ≠ 40 = 0.05, two-tailed test X 44 40 4 6 0.67 6 X 1 Go to the unit normal table, look up z=0.67, p= 0.2514 This is not in the critical region (+ 1.96), so we fail to reject the H0 This means that, based on the data we do not have support that the treatment has an effect. X 44 (b) a sample of 10 with a mean of 44 H0: The sample has the same mean as the population: = 40 HA: The sample has a different mean as the population: ≠ 40 = 0.05, two-tailed test X 44 40 4 1.90 2.11 6 X 10 Go to the unit normal table, look up z=2.11, p= 0.0174 This is in the critical region (+ 1.96), so we reject the H0 This means that, based on the data we do have support that the treatment has an effect. X 44 3) Twenty-five women between the ages of 70 and 80 were randomly selected from the general population of women their age to take part in a special program to decrease (speed up) reaction time. After the course, the women had an average reaction time of 1.5 seconds. Assume that the mean reaction time for the general population of women of this age group is 1.8, with a standard devation of 0.5 seconds (and assume that the distribution is Normally distributed). Carry out a test of the hypothesis (that they were faster than the general popualtion) with an alpha level of 0.01. H0: The sample has the same mean as the population: > 1.8 HA: The sample has a different mean as the population: < 1.8 = 0.01, one-tailed test X 1.5 1.8 0.3 0.1 3.00 0.5 X 25 Go to the unit normal table, look up z=3.0, p= 0.0013 This is in the critical region (- 2.58), so we reject the H0 This means that, based on the data we do have support that the women were faster after the course. X 1.5