Question

A certain drug is used to treat asthma. In a clinical trial of the drug, 25 of 284 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11% of treated subjects experienced headaches.

Answer 1

Remember that the test statistic for proportion-related hypothesis testing is:

$Z_c=\frac{\hat{p}-p_{}}{\sqrt[]{\frac{p(1-p)}{n}}}$

Using the data displayed, we'll have that:

$\begin{gathered} Z_c=\frac{\hat{p}-p_{}}{\sqrt[]{\frac{p(1-p)}{n}}}\rightarrow Z_c=\frac{(0.0880)-(0.1183)_{}}{\sqrt[]{\frac{(0.1183)(1-(0.1183))}{284}}} \\ \\ \Rightarrow Z_c=-1.5811 \end{gathered}$

We can conclude that the test statistic is:

$Z_c=-1.5811$