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 of 2.5 g. A sample of 35 coins was collected. Those coins have a mean weight of 2.493832 g and a standard deviation of 0.01433g. 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?

Explanation / Answer

ho: mean weight equal to 2.5 g

h1; mean weight NOT equal to 2.5 g

test statistic, z = (mean-u)/(sd/sqrt(n)) = (2.493832-2.5)/(.01433/sqrt(35)) = -2.5464

p-value = 2*(1-P(Z<2.5464) = .010883

with t = -2.54 and p-vaue < 0.05, i reject ho at 5% level of significance and conclude that mean weight NOT equal to 2.5 g

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