Question

1)

The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 42 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.211 mm and sample standard deviation 0.009 mm.

Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.1 significance level.

(a) Identify the correct alternative hypothesis HaHa:

• μ<21.21μ<21.21
• μ>21.21μ>21.21
• μ=21.21μ=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:

• Reject H0H0
• Fail to reject H0H0

(e) Explain your choice in the box below.



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

• The sample data supports the claim
• There is not sufficient evidence to warrant rejection of the claim
• There is sufficient evidence to warrant rejection of the claim
• There is not sufficient evidence to support the claim

(g) Explain your choice in the box below.

Answer 1

μ = 21.21, n = 42, x = 21.211, s = 0.009, significance level = 0.1, Degrees of freedom: df = n-1 = 41

a) H₀: μ = 21.21, H_a: μ > 21.21

b) Test statistic: t = (x-μ)/(s/n^0.5) = (21.11-21.21)/(0.009/42^0.5) = -72.0082

c) Critical value (Using Excel function ABS(T.INV(probability,df))) = ABS(T.INV(0.1,41)) = 1.3025

d) Fail to reject H0

e) Since test statistic is less than critical value, we fail to reject H0.

f) There is sufficient evidence to warrant rejection of the claim

g) Since test statistic is less than critical value, we fail to reject H0. so μ = 21.21 and the claim is rejected.