Question

An 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 7.1 lbs/square inch. Assume the variance is known to be 0.81. If the valve was designed to produce a mean pressure of 7.3lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications?

State the null and alternative hypotheses for the above scenario.

Answer 1

Solution :

Given that

= 7.1

² = 0.81

= ² = 0.81 = 0.9

n = 120

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   7.3

H_a : < 7.3

Test statistic = z

= ( - ) / / n

= (7.1 - 7.3) / 0.9 / 120

= -2.43

p(Z < -2.43)

P-value = 0.0075

= 0.1

P-value <

Reject the null hypothesis, because p-value less than 0.1 significance level

Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications