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.)
Answer
The test statistic is \(\boxed{0.20}\).
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 \(\boxed{0.20}\).
