Question

To evaluate the effectiveness of a new type of dental anesthetic, a dentist conducted an experiment with 25 randomly selected patients. Fourteen patients were randomly assigned to receive the standard anesthetic (Novacaine) , while the remaining eleven patients received the proposed new anesthetic. While being treated, each patient was asked to give a measure of his or her discomfort, on a scale from 0 to 100. The patients who received the standard anesthetic had a mean discomfort score of 51.8 with a standard deviation of 12.4, while the patients who received the proposed new anesthetic had a mean discomfort score of 34.4 with a standard deviation of 7.7. Use these data to construct a 90% confidence interval for the difference in the mean discomfort scores for the two types of anesthetic.

Answer 1

The standard error here is computed as:

For n1 + n2 - 2 = 23 degrees of freedom, we get from the t distribution tables here:
P( t23 < 1.714) = 0.95

Therefore, due to symmetry, we get here:
P( - 1.714 < t23 < 1.714) = 0.9

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval for the difference in means here.