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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.

Answer :

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

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