Question

A study randomly assigned resident physicians to either accept free drug samples or refuse them. The researchers then examined prescriptions for drugs that are available both by prescription and in an over-the-counter (OTC) version. Of the 203 relevant prescriptions written by physicians accepting free samples, 52 stipulated the OTC version. Of the 187 relevant prescriptions written by physicians refusing free samples, 75 stipulated the OTC version. Consider these data as two random samples from the populations of prescriptions written by resident physicians with or without access to free samples. Is there good evidence that physicians prescribe proportionally fewer OTC versions when they receive accept samples?

Let p_A be the proportion of OTC prescriptions from physicians accepting free samples
Let p_R be the proportion of OTC prescriptions from physicians refusing free samples

The hypotheses to be tested are:

H0: pA ≥ pR versus Ha: pA < pR

a)  What is the test statistic? Please use 2 decimal places

b) What is the p-value? Please use 4 decimal places.

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Answer 1

From the given information,

By using calculator,

The required correct answers are,

a. Test statistic= -3.05

b. P-value= 0.0011

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