Problem 8 Are Quarters Now Lighter? Weights of quarter are carefully considered in the design of the vending machines that we have all come to know and love. From a data set that contains the weights...

Problem 8
Are Quarters Now Lighter?
Weights of quarter are carefully considered in the design of the vending
machines that we have all come to know and love. From a data set that contains
the weights of a sample of pre-1964 quarters and the weights of a sample of
post-1964 quarters, we obtained the following information:
Pre-1964 Quarters Post-1964 Quarters
40
6.19267 g
0.08700 g
n
x
s
=
=
=
40
5.63930 g
0.06194 g
n
x
s
=
=
=
a. Use a 0.05 significance level to test the claim that pre-1964 quarters have
a mean weight that is greater than the mean weight of post-1964 quarters.
(State your null and alternatively hypothesis, determine the test statistics,
critical value, make a decision, and write the final conclusion.)
b. Construct a confidence interval appropriate for the hypothesis test in part
(a. Based on the confidence interval, do post-1964 quarters appear to
weight less than before 1964? ). Use symbols and words to express your
answer.