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 6.2 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 6.1 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications?

State the null and alternative hypotheses for the above scenario.

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 6.1lbs/square inch.

Alternative hypothesis: Ha: The average water pressure on automobile engines is greater than 6.1 lbs/square inch.

H0: µ = 6.1 versus Ha: µ > 6.1

This is an upper tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 6.1

Xbar = 6.2

σ = 0.8

n = 280

α = 0.05

Z = (6.2 - 6.1)/(0.8/sqrt(280))

Z = 2.09165

P-value = 0.018235

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the average water pressure on automobile engines is greater than 6.1 lbs/square inch.