Question

The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 39 nickles was drawn from a reported defective coin counter machine located near a school. The sample had a sample mean of 21.21 mm and sample standard deviation 0.011 mm. Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.01 significance level.

(a) Identify the correct alternative hypothesis :

μ < 21.21

μ = 21.21

μ > 21.21

Give all answers correct to 4 decimal places.

(b) The test statistic value is:

(c) Using the Traditional method, the critical value is:

(d) Based on your answers above, do you:

(i) Reject Ho

(ii) Fail to reject Ho.

Explain your choice in the box below.

e) Based on your work above, choose one of the following conclusions of your test:

(i) the sample data supports the claim,

(ii) there is not sufficient evidence to support the claim,

(iii) there is sufficient evidence to warrant rejection of the claim

(iv) there is not sufficient evidence to warrant rejection of the claim.

Explain your choice in the box below.

Answer 1

Here in this scenario our claim is that the that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm.

To test the claim we selected 39 sample and found that the sample mean of nickel is 21.21 mm and sample Standerd deviation is 0.011mm.

Here we have to use one sample t test for testing the claim at 0.01 level of significance.

Further the test is performed as below,

a)The alternative hypothesis is Option C .

b) The test Statistic value is 0.

c) Using traditional method the t critical value is 2.429.

t critical value is calculated using t table or using Excel.at t 0.01, at 39-1 degrees of freedom.

Now,

d) based on given test ,

We fail to Reject Ho null hypothesis.

e) Correct option is 2) there is not sufficient evidence to support the claim.

The mean nickel diameter accepted by this coin-counter machine is not greater than 21.21 mm.

Thank you.