Answered

IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 7.6 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 7.5 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Sagot :

Answer:

z(s) =  - 2,15 We accept H₀

Step-by-step explanation:

Assume Normal Distribution.

Sample size                  n = 290

Sample mean               μ = 7,6

Sample standard deviation   s = 0,8

Level of significance  0,02   ( CI = 98 % )

population mean  μ₀ = 7,5

α = 0,02       the valve could fail under and above the spec value ( 7,6 ) therefore we must develop a two-tail test

α/2  =  0,01

Hypothesis Test

Null hypothesis                                      H₀       μ   =  μ₀

Alternative Hypothesis                         Hₐ        μ   ≠  μ₀

for  α  =  0,01    z(c)  = - 2,3

To calculate  z(s)

z(s)  =  ( μ   -  μ₀ ) / s/√n

z(s)  =  ( 7,5 - 7,6 ) /0,8/√290

z(s) = - 0,1 * 17 /0,8

z(s) =  - 1,7 / 0,8

z(s) =  - 2,15

Comparing   z(s)  and  z(c)

- 2, 15  < - 2,3

|z(s)|  <  | z(c)|

Then z(s) is in the acceptance region. We don´t have evidence to reject H₀

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.