Question

claim: the mean systolic blood pressure of all healthy adults is less than than 122 mm hg. sample data: for 280 healthy adults, the mean systolic blood pressure level is 121.69 mm hg and the standard deviation is 15.54 mm hg. the null and alternative hypotheses are ( h_0: mu = 122 ) and ( h_1: mu < 122 ). find the value of the test statistic. the value of the test statistic is (round to two decimal places as needed)

Explanation:

Step1: Identify the formula for the test statistic

When the population standard deviation \(\sigma\) is unknown (here we use sample standard deviation \(s\) as an estimate since \(n = 280\geq30\), we can use the z - test statistic formula \(z=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\)

Step2: Substitute the given values into the formula

We are given \(\bar{x}=121.69\), \(\mu = 122\), \(s = 15.54\), and \(n=280\)

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Answer:

\(-0.33\)