According to the Kaiser Family Foundation, U.S. workers who had employer-provided health insurance paid an average premium of $1170 for single (one person) health insurance coverage during 2013 (www.kff.org). Suppose that a recent random sample of 100 workers with employer-provided health insurance selected from a large city paid an average premium of $1198 for single health insurance coverage. Assume that such premiums paid by all such workers in this city have a standard deviation of $125.
a. Using the critical-value approach and a 1% significance level, can you conclude that the current average such premium paid by all such workers in this city is different from $1170?
b. Using the critical-value approach and a 2.5% significance level, can you conclude that the current average such premium paid by all such workers in this city is higher than $1170?
c. What is the Type I error in parts a and b? What is the probability of making this error in each of parts a and b?
d. Calculate the p-value for the test of part a. What is your conclusion if α = .01?
e. Calculate the p-value for the test of part b. What is your conclusion if α = .025?