Question

A coin mint has a specification that a particular coin has a mean weight of 3.5g. A sample of 36 coins was collected. Those coins have a mean weight of 2.49585g and a standard deviation of 0.01855g. 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 the specifications of the coin mint? a)What are the hypotheses? b)Identify the test statistic? c)Identify the p-value? d)State the final conclusion that addresses the original claim? e)Do the coins appear to conform to the specifications of the coin mint?

Answer 1

Solution:

(Part a)

Here, we have to use one sample t test for the population mean.

Null hypothesis: H₀: The sample is from a population with a mean weight equal to 2.5g.

Alternative hypothesis: H_a: The sample is not from a population with a mean weight equal to 2.5g.

H₀: µ = 2.5 versus H_a: µ ≠ 2.5

This is a two tailed test.

We are given

Level of significance = α = 0.05

Xbar = 2.49585

S = 0.01855

n = 36

df = n – 1 = 36 – 1 = 35

Critical values = -2.0301 and 2.0301

(by using t-table)

(Part b)

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (2.49585 – 2.5)/[0.01855/sqrt(36)]

t = (2.49585 – 2.5)/ 0.0031

t = -1.3423

(Part c)

P-value = 0.1881

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

(Part d)

There is sufficient evidence to conclude that sample is from a population with a mean weight equal to 2.5g.

(Part e)

Yes, the coins do appear to confirm to the specifications of the coin mint because we conclude that the sample is from a population with a mean weight equal to 2.5g.