Question

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

Answer 1

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 =
`(5 - 5.1)/(1/√(120) )`

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