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\( 1 \leftarrow \quad \begin{array}{l}\text { A certain drug is used to treat asthma. In a clinical trial of the drug, } 28 \text { of } 290 \text { treated subjects experienced } \\ \text { headaches (based on data from the manufacturer). The accompanying calculator display shows results } \\ \text { from a test of the claim that less than } 10 \% \text { of treated subjects experienced headaches. Use the normal } \\ \text { distribution as an approximation to the binomial distribution and assume a } 0.05 \text { significance level to } \\ \text { complete parts (a) through (e) below. }\end{array} \)\begin{tabular}{|c}\( 1- \) PropzTest \\ prop \( <0.1 \) \\ \( z=-0.195740073 \) \\ \( p=0.4224068087 \) \\ \( \hat{p}=0.0965517241 \) \\ \( n=290 \)\end{tabular} a. Is the test two-tailed, left-tailed, or right-tailed? Right tailed test Two-tailed test b. What is the test statistic? z= (Round to two decimal places as needed.)

Ask by Medina Delgado. in the United States
Mar 13,2025

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**(a)** The test is a left-tailed test. **(b)** The test statistic \( z \) is **-0.19**.

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The Deep Dive

The test is left-tailed since we are testing the claim that less than 10% of treated subjects experienced headaches. It specifically investigates whether the proportion of subjects experiencing headaches is significantly lower than the hypothesized proportion. The test statistic given in the data is \( z = -0.20 \) when rounded to two decimal places. This z-score indicates how many standard deviations the sample proportion is below the hypothesized proportion of 10%.

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