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A new dental bonding agent. Refer to the Trends in
Chapter 7, Problem 90E(choose chapter or problem)
A new dental bonding agent. Refer to the Trends in Biomaterials & Artificial Organs (Jan. 2003) study of a new dental bonding adhesive (called Smartbond), Exercise 7.54 (p. 385). Recall that tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of \(\bar{x}=5.07\) Mpa and a standard deviation of s = .46 Mpa. The manufacturer must demonstrate that the breaking strength variance of the new adhesive is less than the variance of the standard composite adhesive, \(\sigma^2=.25\).
a. Set up the null and alternative hypotheses for the test.
b. Find the rejection region for the test using \(\alpha=.01\).
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?
Questions & Answers
QUESTION:
A new dental bonding agent. Refer to the Trends in Biomaterials & Artificial Organs (Jan. 2003) study of a new dental bonding adhesive (called Smartbond), Exercise 7.54 (p. 385). Recall that tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of \(\bar{x}=5.07\) Mpa and a standard deviation of s = .46 Mpa. The manufacturer must demonstrate that the breaking strength variance of the new adhesive is less than the variance of the standard composite adhesive, \(\sigma^2=.25\).
a. Set up the null and alternative hypotheses for the test.
b. Find the rejection region for the test using \(\alpha=.01\).
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:Solution :
Step 1 of 5:
Given the mean of the strength is Mpa and
The standard deviation is s=0.46 Mpa.
Then the manufacturer must demonstrate that the breaking strength of the new adhesive is less than the variance of the standard deviation composite adhesive, .
Our goal is :
a). We need to set up the null and alternative hypothesis for the test.
b). We need to find the rejection for the test using .
c). We need to compute the test statistic.
d). We need to give the appropriate conclusion for the test.
e). We need to find what condition are required for the test results to be valid.
a). Now we have to set up the null and alternative hypothesis for the test.
We know that the manufacturer must demonstrate that the breaking strength of the new adhesive is less than the variance of the standard deviation composite adhesive, .
Then the null and alternative hypothesis are
againest