A certain drug is used to treat asthma. In a clinical trial of the drug, 28 of 290 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 0.05 significance level to complete parts (a) through (e) below. 1-PropZTest prop \( <0.1 \) \( z=-0.195740073 \) \( p=0.4224068087 \) \( \hat{p}=0.0965517241 \) \( \mathrm{n}=290 \) 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? \[ \mathrm{z}=\square \] (Round to two decimal places as needed.)

The test is a left-tailed test because the claim being tested is whether the proportion of subjects experiencing headaches is less than \( 10\% \), which corresponds to a direction. The test statistic calculated is \( z \approx -0.20 \) when rounded to two decimal places. This indicates that the sample proportion is slightly below the hypothesized proportion of \( 10\% \). Now, just for some added context, in hypothesis testing, a left-tailed test like this one seeks to determine if a certain parameter is significantly lower than a specified value, which can provide essential insights into the effectiveness of treatments like the asthma drug. On a practical note, understanding test statistics helps researchers and healthcare professionals make informed decisions based on data. If your null hypothesis (that the true proportion of headaches is \( \geq 0.10 \)) is refuted, doctors may encourage more patients to use the treatment, improving the quality of asthma care!