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 5 of 5: enter the conclusion. answer 1 point tables keypad keyboard shortcuts reject null hypothesis fail to reject null hypothesis

Explanation:

Step1: State the hypotheses

$H_0:\mu = 5.3$ (null hypothesis), $H_1:\mu>5.3$ (alternative hypothesis)

Step2: Calculate the 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 $\bar{x} = 5.5$, $\mu = 5.3$, $\sigma = 1.0$, and $n = 180$.
$z=\frac{5.5 - 5.3}{\frac{1.0}{\sqrt{180}}}\approx\frac{0.2}{\frac{1.0}{13.4164}}\approx 2.68$

Step3: Find the critical value

For a one - tailed test with $\alpha=0.02$, the critical value $z_{\alpha}$ from the standard normal distribution table is approximately $2.05$.

Step4: Make a decision

Since the calculated $z$ - value ($2.68$) is greater than the critical value ($2.05$), we reject the null hypothesis.

Answer:

Reject Null Hypothesis