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 36 coins was collected. Those coins have a mean weight of 2.49502g and a standard deviation of 0.01562

Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g

Do the coins appear to conform to the specifications of the coin​ mint?

test statistic z=

p=

Answer 1

Since we need to test the claim that the mean is equal to 2.5 gms, we use a 2 tailed test.

Given: = 2.5 gms, = 0.01562 gms, = 2.49502 gms, n = 36, = 0.05

The Hypothesis:

H0: = 2.5 gms

Ha: 2.5 gms

This is a Left Tailed Test.

The Test Statistic: Although the population standard deviation is unknown, we use the students z test as sample size is > 30 and its normally distributed.

The test statistic is given by the equation:

The p Value:    The p value for Z = -1.91. Since this is a 2 tailed test, we calculate the left tailed probability from the normal distribution as 0.02807. Therefore the 2 tailed probability = 2 * 0.02807. Therefore the p value = 0.0561

The Decision Rule:   If P value is < , Then Reject H0.

The Decision:   Since P value (0.0561) is > (0.05) , We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that the mean weight is not 2.5 gms. i.e there is not sufficient evidence that the coins does not conform to the specifications of the coin mint.