Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 250 engines and the mean pressure was 7.8 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 7.9 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs below the specifications?

State the null and alternative hypotheses for the above scenario.

Answer 1

Solution:

For the given scenario, we need to use the one sample z test for the population mean, because we are given the value for the population standard deviation. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The mean pressure of the valve is 7.9 lbs/square inch.

Alternative hypothesis: Ha: The mean pressure of the value is less than 7.9 lbs/square inch.

H0: µ = 7.9 versus Ha: µ < 7.9

This is a lower tailed or left tailed test.