The engineer designed the valve such that it would produce a mean pressure of 5.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 6 engines and the mean pressure was 5.4 pounds/square inch with a standard deviation of 0.7. 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.

The calculated value  t = 1.399 < 2.5705 at 0.025 level of significance

Null hypothesis is accepted

The population distribution is approximately normal

Step-by-step explanation:

Step(i):-

Given mean of the Population = 5.0

sample size 'n'= 6

The mean of the sample x=5.4 pounds /square inch

The standard deviation of the sample (S) = 0.7

Level of significance = 0.025

Null Hypothesis : The sample came from population

H₀ : x⁻ = μ

Alternative Hypothesis :H₁ : x⁻ ≠ μ

Step(ii):-

Test statistic

                     t = 1.399

Degrees of freedom = n-1 =6-1 =5

The tabulated value

                  t = 2.5705

The calculated value  t = 1.399 < 2.5705 at 0.025 level of significance

Null hypothesis is accepted

The population distribution is approximately normal

incomplete question. how do you expect anyone to you when you do not post the question in its entirety?