Question

n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 9 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.81. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

The calculated t- value = 1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4

Explanation:

Step(i):-

Given mean of the Population (μ) = 5.4

Given sample size 'n' = 9

Mean of the sample (x⁻) = 5.7

Standard deviation of the sample (s) = 0.81

Step(ii):-

Null Hypothesis: H₀: The engineer designed the valve such that it would produce a mean pressure of 5.4

H₀: μ = 5.4

Alternative Hypothesis : H₁: μ ≠ 5.4

Level of significance = 0.025

Test statistic

`t = (x^(-) -mean)/((S)/(√(n) ) )`

`t = (5.7 -5.4)/((0.81)/(√(9) ) )`

t = 1.11

Degrees of freedom

ν = n-1 = 9-1 =8

t₀.₀₁₅ , ₈ = 2.89

The calculated t- value = 1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4