When bonding teeth, orthodontists must maintain a dry field. A new bonding adhes

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 a concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 14 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of 2.71 MPa, and a standard deviation of 3.5 MPa. Orthodontists want to know if the true mean breaking strength is less than 4.58 MPa, the mean breaking strength of the composite adhesive. Assume normal distribution for breaking strength of the new adhesive.

1) What are the appropriate hypotheses one should test? Correct: H0:?=4.58 against Ha:?<4.58.

2) The formula of the test-statistic to use here is Correct: x¯??0s/n?.

3)Rejection region: We should reject H0 at 2.5% level of significance if:

a) |test statistic| >2.241. b) test statistic <?1.960. c) test statistic <?2.160. d) test statistic >2.160. e)test statistic >1.960. f) |test statistic| >2.533.

4)The value of the test-statistic is (answer to 3 decimal places):

If ?=0.025, what will be your conclusion? Correct: Do not reject H0.

5) The p-value of the test is (answer to 4 decimal places):

6)We should reject H0 for all significance level which are Correct: larger than p-value. Incorrect not equal to p-value.

Explanation / Answer

3)Rejection region: We should reject H0 at 2.5% level of significance if:

c) test statistic <?2.160.

4)The value of the test-statistic is (answer to 3 decimal places): t=-1.999

If ?=0.025, what will be your conclusion? Do Not reject H0.

5) The p-value of the test is (answer to 4 decimal places):0.0335.

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