Problem
A certain drug is used to treat asthma. In a clinical trial of the drug, 29 of 280 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 $10 \%$ of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below. \[ \begin{array}{|l|} \hline \text { 1-PropZTest } \\ \text { prop }<0.1 \\ z=0.199204768 \\ p=0.5789487151 \\ \hat{p}=0.1035714286 \\ n=280 \end{array} \] a. Is the test two-tailed, left-tailed, or right-tailed? Left-tailed test Right tailed test Two-tailed test b. What is the test statistic? $z=$ (Round to two decimal places as needed.)
Solution
Step 1 ：The test is for the claim that less than 10% of treated subjects experienced headaches. This indicates a left-tailed test.
Step 2 ：The test statistic is given in the problem statement as z=0.199204768. We need to round this to two decimal places.
Step 3 ：The test is a \(\boxed{\text{left-tailed test}}\).
Step 4 ：The test statistic is \(\boxed{0.20}\).
