Question 1 of 11, Step 2 of 6
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An engineer has designed a valve that will regulate water pressure on an automoble engine. The valve was tested on 180 engines and the mean pressure was 4.6 pounds/square inch (psi). Assume the population standard deviation is 0.5 . If the valve was designed to produce a mean pressure of 4.5 psi, is there sufficlent evide the 0.01 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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Step 1 ：The question is asking for the value of the test statistic in a hypothesis testing scenario. The test statistic can be calculated using the formula for a z-score, which is $(\text{sample mean}-\text{population mean})/(\text{standard deviation}/\sqrt{\text{sample size}})$. In this case, the sample mean is 4.6 psi, the population mean (under the null hypothesis) is 4.5 psi, the standard deviation is 0.5, and the sample size is 180.

Step 2 ：Let's calculate the test statistic using these values. The sample mean is 4.6, the population mean is 4.5, the standard deviation is 0.5, and the sample size is 180.

Step 3 ：The test statistic is calculated to be approximately 2.68. This is the value of the z-score that we would compare to a critical value to determine whether to reject the null hypothesis.

Step 4 ：Final Answer: The value of the test statistic is approximately $\boxed{{\displaystyle 2.68}}$.