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 9 extracted teeth bonded with the new adhesive resulted in a mean breaking strength​(after 24​ hours) of overbar x=5.78 Mpa and a standard deviation of s=0.41 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.35 ​Mpa, the mean breaking strength of the composite adhesive.

A) We must assume that the sample was not random and selected from a population with a highly skewed distribution.

B.)We must assume that the sample was random and selected from a population with a distribution that is approximately normal.

C.)We must assume that the sample was not random and selected from a normally distributed population.

D).We must assume that the sample was random and selected from a population that is highly skewed.

Answer 1

Let denote the true mean breaking strength.

We have to test:

Vs

For a small sample ( n = 9) and for unknown population variance, (since, we only have the mean and standard deviation of the sample), the appropriate statistic to be used here is given by:

The use of t test requires the following pre-requisites or assumptions:

- The data must be normally distributed

Only then can we claim that and hence, derive the test statistic t

- The data is collected from a representative, randomly selected portion of the total population.

Otherwise the measures mat not be reliable as they may be biased due to non-representatives of the sample , based on which these measures are computed.

Hence, to test the claim,

B.)We must assume that the sample was random and selected from a population with a distribution that is approximately normal.