The physician-recommended dosage of a new medication is 14 mg. Actual administered doses vary slightly from dose to dose and are Normally distributed, with mean μ. A representative of a medical review board wishes to see if there is any evidence that the mean dosage is more than recommended and so intends to test the following hypotheses:
H₀: μ= 14 versus H_a: μ> 14
To do this, he selects 16 doses at random and determines the weight of each. He finds the sample mean to be x̄= 14.12 mg and the sample standard deviation to be σ= 0.24 mg.
Suppose we were not sure if the distribution of weights was Normal. In which of the following circumstances would we NOT be safe using a t procedure in this scenario?

Question

Quizplus · Accepted Answer

The presence of a large outlier can strongly affect the validity of using a t-procedure, as it can impact the assumptions of normality and independence required for the test. If there is a large outlier, it may be necessary to consider a non-parametric test or to remove the outlier before proceeding with the t-test. The other factors (mean and median nearly equal, moderate skewness, and large sample standard deviation) do not necessarily preclude the use of a t-procedure, as long as other assumptions such as normality and independence are met.

The Physician-Recommended Dosage of a New Medication Is 14 Mg