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 37 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.212 mm and sample standard deviation 0.01 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 Ha :μ > 21.21 μ < 21.21 μ = 21.21Give 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:Fail to reject H 0 Reject H 0(e) Explain your choice in the box below.(f) Based on your work above, choose one of the following conclusions of your test: There is sufficient evidence to warrant rejection of the claim There is not sufficient evidence to warrant rejection of the claim There is not sufficient evidence to support the claim The sample data supports the claim(g) Explain your choice in the box below.

Answer 1

μ > 21.21

Test statistic = 1.217

Kindly check explanation for more details

Explanation:

The null hypothesis, H0 : μ = 21.21

Alternative hypothesis, H1 : μ > 21.21

The test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(21.212 - 21.21) ÷ (0.01 / √2)

= 1.217

The critical value :

From the t distribution :, one tailed = 2.434

Decision region :

Reject H0 if test statistic > critical value

1.217 < 2.434 ; We fail to reject the null ` ; and conclude that there is not enough evidence to support the claim.