According to an estimate, the average age at first marriage for men in the United States was

Question:

According to an estimate, the average age at first marriage for men in the United States was 28.2 years in 2010 (Time, March 21, 2011). A recent sample of 200 men from Ohio who got married for the first time this year showed that their average age at first marriage was 27.1 years. Assume that the population standard deviation for the of ages at first marriage of all men from Ohio who got married for the first time this year is 5.8 years.
a. Using the critical-value approach, can you conclude that the average age at first marriage for all men from Ohio who got married for the first time this year is lower than 28.2 years? Use α = .01.
b. What is the Type I error in part a? Explain. What is the probability of making this error in part a?
c. Will your conclusion of part a change if the probability of making a Type I error is zero?
d. Calculate the p-value for the test of part a. What is your conclusion if α = .01?
Distribution
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