Question

When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smartbond) has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 12 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x = 5.44 Mpa and a standard deviation of s = .38 Mpa. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 6.07 Mpa, the mean breaking strength of the composite adhesive.

a.) Set up the null and alternative hypotheses for the test.

b.) Find the rejection region for the test using α = .01.

c.) Compute the test statistic.

d.) Give the appropriate conclusion for the test.

e.) What conditions are required for the test results to be valid?

Answer 1

Solution :

= 6.07

= 5.44

s = 0.38

n = 12

This is the left tailed test .

The null and alternative hypothesis is

H0 :   = 6.07

Ha : < 6.07

= 0.01  

The critical value for a left-tailed test is tc​=−2.718.

Rejection region = t<−2.718

Test statistic = t

= ( - ) / s / n

= (5.44 - 6.07) /0.38 / 12

= -5.743

P (t< -5.743 ) = 0.0001

P-value = 0.0001

= 0.01  

0.0001< 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that because p-value less than .