Question

An engineer has designed a valve that will regulate water pressure on an automobile engine.  The valve was tested on 220 engines and the mean pressure was 5.8 lbs/square inch.  Assume the standard deviation is known to be 0.6.  If the valve was designed to produce a mean pressure of 5.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average water pressure on automobile engines is 5.7 lbs/square inch.

Alternative hypothesis: H_a: The average water pressure on automobile engines is different than 5.7 lbs/square inch.

H₀: µ = 5.7 versus H_a: µ ≠ 5.7

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 5.7

Xbar = 5.8

σ = 0.6

n = 220

α = 0.02

Critical value = - 2.3263 and 2.3263

(by using z-table or excel)

Z = (5.8 – 5.7)/[0.6/sqrt(220)]

Z = 2.4721

P-value = 0.0134

(by using Z-table)

P-value < α = 0.02

So, we reject the null hypothesis

There is sufficient evidence to conclude that the average water pressure on automobile engines is different than 5.7 lbs/square inch.

There is sufficient evidence to conclude that the valve does not perform to the specifications.