Problem
Save \& Exit Certify Lesson: 10.2 Hypothesis Testing for Popula.. NYAH GRIME Question 2 of 6, Step 2 of 6 $7 / 36$ Correct An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 6.0 pounds/square inch (psi), Assume the population standard deviation is 0.9 . If the valve was designed to produce a mean pressure of 5.9 psi, is there sufficient evidence at the 0.1 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. Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts Previous step answers
Solution
Step 1 ：Given that the sample mean (X) is 6.0, the hypothesized population mean (μ) is 5.9, the population standard deviation (σ) is 0.9, and the sample size (n) is 210.
Step 2 ：The formula for the test statistic in this case is: \(Z = \frac{(X - μ)}{(σ / \sqrt{n})}\)
Step 3 ：Substitute the given values into the formula: \(Z = \frac{(6.0 - 5.9)}{(0.9 / \sqrt{210})}\)
Step 4 ：Solve the equation to find the value of Z.
Step 5 ：\(Z = 1.6101529717988208\)
Step 6 ：Round the value of Z to two decimal places.
Step 7 ：Final Answer: The value of the test statistic, rounded to two decimal places, is \(\boxed{1.61}\)
