Question

an engineer designed a valve that will regulate water pressure on an automobile engine. the engineer designed the valve such that it would produce a mean pressure of 5.3 pounds/square inch. the valve was tested on 180 engines and the mean pressure was 5.5 pounds/square inch. assume the standard deviation is known to be 1.0. is there evidence at the 0.02 level that the valve performs above the specifications? step 2 of 5: enter the value of the z - test statistic. round your answer to two decimal places.

Explanation:

Step1: Recall z - test formula

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

Step2: Identify the values

We are given that $\bar{x} = 5.5$, $\mu=5.3$, $\sigma = 1.0$, and $n = 180$.

Step3: Substitute values into the formula

$z=\frac{5.5 - 5.3}{\frac{1.0}{\sqrt{180}}}=\frac{0.2}{\frac{1.0}{\sqrt{180}}}$. First, calculate $\frac{1.0}{\sqrt{180}}\approx\frac{1.0}{13.4164}\approx0.0745$. Then, $z=\frac{0.2}{0.0745}\approx2.68$.

Answer:

$2.68$