Assume that a simple random sample has been selected from anormally distributed population and test the given claim. Identifythe null and alternative​ hypotheses, test​ statistic, P-value, andstate the final conclusion that addresses the original claim.
A coin mint has a specification that a particular coin has amean weight of 2.5 g. A sample of 33 coins was collected. Thosecoins have a mean weight of 2.49554 g and a standard deviation of0.01347 g. Use a 0.05 significance level to test the claim thatthis sample is from a population with a mean weight equal to 2.5 g.Do the coins appear to conform to the specifications of the coin​mint?
Identify the test statistic.
t=?
​(Round to three decimal places as​ needed.)
Identify the​ P-value.
The​ P-value is ?.
​(Round to four decimal places as​ needed.)
State the final conclusion that addresses the original claim.Choose the correct answer below.
A. Fail to reject Upper H 0. There is sufficient evidence towarrant rejection of the claim that the sample is from a populationwith a mean weight equal to 2.5 g.
B. Reject Upper H 0. There is sufficient evidence to warrantrejection of the claim that the sample is from a population with amean weight equal to 2.5 g.
C. Fail to reject Upper H 0. There is insufficient evidence towarrant rejection of the claim that the sample is from a populationwith a mean weight equal to 2.5 g.
D. Reject Upper H 0. There is insufficient evidence to warrantrejection of the claim that the sample is from a population with amean weight equal to 2.5 g.
Do the coins appear to conform to the specifications of thecoin​ mint?
A. No, since the coins seem to come from a population with amean weight different from 2.49554 g.
B. Yes, since the coins do not seem to come from a populationwith a mean weight different from 2.5 g.
C. Yes, since the coins do not seem to come from a populationwith a mean weight different from 2.49554 g.
D. No, since the coins seem to come from a population with amean weight different from 2.5g.
E. The results are inconclusive because individual differencesin coin weights need to be analyzed further.
