Question

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 4.7 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 4.8 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? Find the p-value of the test statistic. Round your answer to four decimal places.

Answer 1

To determine if the valve performs to specifications, conduct a hypothesis test using a one-sample z-test. Calculate the test statistic using the formula z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). Find the p-value by looking up the corresponding area in the standard normal distribution table.

Step-by-step explanation:

To determine if the valve performs to specifications, we can conduct a hypothesis test. We will use a one-sample z-test comparing the mean pressure of the tested valves to the designed mean pressure. The null hypothesis (H0) is that the mean pressure is equal to 4.8 psi, and the alternative hypothesis (Ha) is that the mean pressure is not equal to 4.8 psi.

To calculate the test statistic, we use the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). Substituting the given values, we get z = (4.7 - 4.8) / (1.0 / sqrt(210)).

From the z-test, we find that the test statistic is -3.07. To find the p-value, we look up the corresponding area in the standard normal distribution table. The p-value for a test statistic of -3.07 is approximately 0.0014 (rounded to four decimal places).