Question

claim: the mean systolic blood pressure of all healthy adults is less than than 125 mm hg. sample data: for 286 healthy adults, the mean systolic blood pressure level is 124.57 mm hg and the standard deviation is 15.07 mm hg. the null and alternative hypotheses are ( h_0: mu = 125 ) and ( h_1: mu < 125 ). find the value of the test statistic.
the value of the test statistic is (square)
(round to two decimal places as needed)

Explanation:

Step1: Recall the formula for the z - test statistic

The formula for the z - test statistic when testing a hypothesis about a population mean (assuming the population standard deviation \(\sigma\) is known) is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\)

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

We are given that \(\bar{x} = 124.57\), \(\mu = 125\), \(\sigma=15.07\), and \(n = 286\)

Step3: Substitute the values into the formula

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Answer:

\(-0.48\)