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

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.)

Accepted Answer

# 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
$$
\begin{align*}
z&=\frac{118.54 - 119}{\frac{15.03}{\sqrt{281}}}\
&=\frac{- 0.46}{\frac{15.03}{16.763}}\
&=\frac{-0.46}{0.896}\
&\approx - 0.51
\end{align*}
$$

# Answer:
$-0.51$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the test statistic

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

Step3: Substitute the values into the formula

Answer: