Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 190 engines and the mean pressure was 6.9 pounds/square inch (psi). Assume the population standard deviation is 0.7. If the valve was designed to produce a mean pressure of 7.0 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

To test whether the valve performs to the specifications, a one-sample t-test is conducted using the given data. The test statistic is calculated using the formula t = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). The calculated test statistic falls outside the critical region, indicating sufficient evidence to conclude that the valve does not perform to the specifications.

Step-by-step explanation:

To test whether the valve performs to the specifications, we can conduct a one-sample t-test. The null hypothesis is that the mean pressure is equal to 7.0 psi, while the alternative hypothesis is that the mean pressure is not equal to 7.0 psi. We'll use a significance level of 0.05.

To calculate the test statistic, we can use the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the values, we have:

t = (6.9 - 7.0) / (0.7 / sqrt(190)) = -4.07

The absolute value of the test statistic is 4.07. Since the t-value falls outside the critical region (-1.96 to 1.96 for a two-tailed test at a 0.05 level of significance), we can reject the null hypothesis. Therefore, there is sufficient evidence to conclude that the valve does not perform to the specifications.