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Lesson: 10.2 Hypothesis Testing for Popula..
NYAH GRIME
Question 2 of 6, Step 2 of 6
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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.
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Final Answer: The value of the test statistic, rounded to two decimal places, is \(\boxed{1.61}\)
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 \(\boxed{1.61}\)
