Question

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 33 coins was collected. Those coins have a mean weight of 2.49554 g and a standard deviation of 0.01347 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?

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 to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

B. 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. 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.

D. 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.

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 2.49554 g.

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

C. Yes, since the coins do not seem to come from a population with a mean weight different from 2.49554 g.

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

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

Answer 1

Given: = 2.5, = 2.49554, s = 0.01347, n = 33, = 0.05

The Hypothesis:

H0: = 2.5

Ha: 2.5

This is a 2 tailed test

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The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

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The p Value:    The p value for t = -1.902, for degrees of freedom (df) = n-1 = 32, is; p value = 0.0662

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The Decision: Since p value is >

Option C: Fail to Reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight of 2.5.

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Do the coins appear to confirm? Option B: Yes, since the coins do not seem to come from a population with a mean weight different from 2.5 g.

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