Assume that a simple random sample has been selected from a normally distributed

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 at 2.5 g. A sample at 35 coins was collected. Those coins have a mean height at 2.45657 g and a standard deviation of 0.01384 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. the coins appear to conform to the specifications of the coin mint? What are the hypothesis? A. H_0: mu = 2.5 g H_1: mu greaterthanorequalto 2.5 g B. H_0: mu = 2.5 g H_1: mu 2.5 g C. H_0: mu notequalto 2.5 g H_0: mu = 2.0 g D. H_0: mu = 2.5 g H_1: mu notequalto 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 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 H_0. There is sufficient evidence to warrant rejection of the claim that the sample is from the population with a mean weight equal to 2.5 g. C. Fail to reject 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 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 populations of the coin mint? A. Yes, since the coins do not seem to come from a population with a mean weight different from 2.5 g. B. Yes, sine the coins do not seem to come from a population with a mean weight different from 2.49557 g. C. No, since the coins seem to come from a population with a mean weight different from 2.0 g. D. No, since the coins seem to come from a population with a mean weight different from 2.45657 g. E. The results are inconclusive because individual differences in coin weights need to be analyzed further.

Explanation / Answer

(first part) right choice is D.H0:mu=2.5g and H1:mu is not equal to 2.5g

(second part) we use z-test as sample size is more than 30 and

z=(xbar-mu)/(sd/sqrt(n))=(2.45657-2.5)/(0.01384/sqrt(35))=-18.56

p-value is <0.0001

(third part) right choice is D. reject H0, there is sufficient evidence.......2.5g

(fourth) right choice is C, No since the coins............2.5g

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