Question

9. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of 2.5 g. A sample of 39 coins was collected. Those coins have a mean weight of 2.49476 g and a standard deviation of 0.01316 g. Use a 0.05 significance level to test the claim that this 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?

What are the​ hypotheses?

A.H 0​: µ = 2.5 g

H 1​: µ ≥ 2.5g

B. H 0​: µ ≠2.5 g

H 1​: µ = 2.5 g

C.H 0​: µ = 2.5 g

H 1​: µ < .5 g

D.H 0​: µ = 2.5 g

     H 1​: µ ≠ 2.5 g

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.Reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

B.Fail to reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

C.Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

D.Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the 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?

A.No, since the coins seem to come from a population with a mean weight different from 2.49618 g.

B.Yes, since the coins do not seem to come from a population with a mean weight different from 2.5 g.

C.No, since the coins seem to come from a population with a mean weight different from 2.5 g.

D.Yes, since the coins do not seem to come from a population with a mean weight different from 2.49618 g.

E.The results are inconclusive because individual differences in coin weights need to be analyzed further.

Answer 1

D option

D.Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

C.No, since the coins seem to come from a population with a mean weight different from 2.5 g.