A random sample of 40 quarters minted after 1964 are weighed. The mean weight is 5.639 grams and the standard deviation is 0.062 gram. Assume that we want to use a 0.05 significance level to test the claim that the population of quarters has a mean weight of 5.670 grams, which is the manufacturing specification.

a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. What is the value of the standard score for the sample mean of 5.639 grams?
d. What is the P-value?
e. What do you conclude? (Be sure to address the original claim that the mean weight is 5.670 grams.)

f. Describe a type I error for this test.
g. Describe a type II error for this test.