Question

question 9 of 13 step 6 of 6 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 6 of 6: make the decision to reject or fail to reject the null hypothesis. answer 1 point tables keypad keyboard shortcuts reject null hypothesis fall to reject null hypothesis

Explanation:

Step1: State the hypotheses

$H_0:\mu = 5.2$ (null hypothesis), $H_1:\mu>5.2$ (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 $\bar{x} = 5.4$, $\mu = 5.2$, $\sigma=0.9$, and $n = 180$.
$z=\frac{5.4 - 5.2}{\frac{0.9}{\sqrt{180}}}=\frac{0.2}{\frac{0.9}{13.4164}}=\frac{0.2}{0.0671}\approx2.98$

Step3: Determine the critical value

For a one - tailed test with $\alpha = 0.05$, the critical value $z_{\alpha}=1.645$

Step4: Make the decision

Since the calculated z - value ($z = 2.98$) is greater than the critical value ($z_{\alpha}=1.645$), we reject the null hypothesis.

Answer:

Reject Null Hypothesis