Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 4.4 lbs/square inch. Assume the standard deviation is known to be 0.8 If the valve was designed to produce a mean pressure of 4.3 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

State the null and alternative hypotheses for the above scenario.

Ho:

Ha:

Answer 1

n = 280, ă = 4.4. 0.8 0.02 - Mo = 4.3 Here n is large population standard deviation is known. Assume sample taken from normally distributed population . Here ye 2 test.

Ho! valve produces a mean pressure of 43 lbs/sq. M = 4.3 Hi: value does not produces a mean pressure 4.3 165/58. 4 & 4.3 L = c - allo oin 4.4 - 4.3 0.8/280 I cal 2.0917 2.0917 Critical value of a at 0.02 level of significane allemative hypothesis 24/2 do.01 = 2. 33

p value = P. (2 72.09.17). p.02 > 2.091.1) +(<-2.0917) 2 P (2 72.0919) 2X 0.0183 . 0.0366 .'. Her p value > x=0.02 Also Ical Len't he do not reject Ho We conclude that value produell..a mean pressure ofi: 4.3. ebs/ square. That iy value perform to the specifications -