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

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