More thanan 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 5 lbs/square inch. assume the variance is known to be 1. if the valve was designed to produce a mean pressure of 5.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? state the null and alternative hypotheses for the above scenario. answer

We accept the null hypothesis

Step-by-step explanation:

Given

The valve was tested on 120 engines

Mean pressure = 5 lbs/square inch.

Variance = 1

Standard Deviation, σ = √1 = 1

The valve was designed to produce a mean pressure of 5.1 lbs/square inch

So, μ = 5.1

Null hypothesis: H₀ : μ = 5.1

Alternative Hypothesis: H₁ : μ≠ 5.1

Since n > 30 and population standard deviation is given

So, We will use z test

Formula : z = (x - μ)/( σ /√n) ---_-_--- Substitute the values

z =

z = −1.1

The p - value of -1.1 (refer to z table) is 0.13576

Since it is a two tailed test So, p = 2(1-  0.13576) = 1.7285

α = 0.02

p value > α

So, we accept the null hypothesis

Hence There is no sufficient evidence at the 0.02 level that the valve does not performs below to the specifications