Question

claim: the mean systolic blood pressure of all healthy adults is less than than 119 mm hg sample data: for 281 healthy adults, the mean systolic blood pressure level is 118.54 mm hg and the standard deviation is 15.03 mm hg the null and alternative hypotheses are ( h_0: mu = 119 ) and ( h_1: mu < 119 ). find the value of the test statistic. the value of the test statistic is (round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the test statistic

The formula for the test statistic \( z\) in a one - sample \( z\) - test (when the population standard deviation \(\sigma\) is known, and here we can use the sample standard deviation \(s\) as an estimate since \(n\) is large (\(n = 281\geq30\)) is \(z=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\)

Step2: Identify the values of \(\bar{x},\mu,s,n\)

We are given that \(\bar{x}=118.54\), \(\mu = 119\), \(s = 15.03\), and \(n=281\)

Step3: Substitute the values into the formula

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Answer:

\(-0.51\)