Question

When bonding​ teeth, orthodontists must maintain a dry field. A new bonding adhesive 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 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength​ (after 24​ hours) of x = 5.42 Mpa and a standard deviation of s = 0.45 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.01 ​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

Answer:

=6.01, s= 0.45, n= 10, = 5.42

a)

null and alternative hypotheses

Ho: 6.01

Ha: < 6.01

b)

now find the t critical value to get rejection region

with left tailed test and df= n-1 = 10 - 1 = 9 and =0.01

using t table we get

critical value = -2.821

Rejection region is: Reject Ho if t < -2.821

c)

formula for test statistics is

t = -4.146

test statistics = -4.146

d)

here ( test statistics = -4.146) < (critical value = -2.821 )

hence, Null Hypothesis is rejected.

Conclusion:

Therefore there is enough sufficient evidence to support the claim that the true mean breaking strength is less than 6.01 ​Mpa.

e)

conditions are as follows

i) sample must be simple random sample.

ii) sample should be taken from normaly distributed population.