Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 6.2 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 6.3 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Let u denotes the population mean. Hypotheses : To test null hypothesis Ho :p =6.3 against alternative hypothesis H1 :: 76.3 Letī denotes the sample mean, o denotes the population standard deviation and n denotes the sample size. Here, x = 6.2000,0° = 0.6400,0 = 0.80, n = 120 The test statistic can be written as: nc - 6.3) which under Ho follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.01 level of significance if P-value < 0.01 or if |zobs > 20.005 = 2.575829 0.4 - 0.3 density 0.2- 0.1 0.0 -2 0 Z Now, Value of test statistic: The value of the test statistic is Zobs = 1206.2000 - 6.3) 0.80 :-1.369306 -1.37 The critical value =+ 2.575829 +2.576 P-value = P(Z > Zobs) = 2 * P(Z < -1.369306) = 2 * 0.085452 = 0.170904 0.1709 Conclusion : Since p-value > 0.01 and |zobs Zcritical = 2.58, so We fail to reject H, at 0.01 level of significance Hence, we can conclude that the population mean is not different from 6.3.