Question

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 180 engines and the mean pressure was 5.4 pounds/square inch (psi). assume the population standard deviation is 0.9. if the valve was designed to produce a mean pressure of 5.2 psi, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? step 2 of 6: find the value of the test statistic. round your answer to two decimal places. answerhow to enter your answer (opens in new window) 1 point tables keypad keyboard shortcuts

Explanation:

Step1: Identify the formula for z - test statistic

The formula for the z - test statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Step2: Substitute the given values

We are given that $\bar{x} = 5.4$, $\mu=5.2$, $\sigma = 0.9$, and $n = 180$.
\[

$$\begin{align*} z&=\frac{5.4 - 5.2}{\frac{0.9}{\sqrt{180}}}\\ &=\frac{0.2}{\frac{0.9}{13.4164}}\\ &=\frac{0.2}{0.0671}\\ &\approx2.98 \end{align*}$$

\]

Answer:

$2.98$