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Answer:
<em>The calculated t- value = 1.11 > 2.89 at 0.025 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given mean of the Population (μ) = 5.4</em>
<em>Given sample size 'n' = 9</em>
<em>Mean of the sample (x⁻) = 5.7</em>
<em>Standard deviation of the sample (s) = 0.81</em>
<u><em>Step(ii):-</em></u>
<em>Null Hypothesis: H₀:</em> The engineer designed the valve such that it would produce a mean pressure of 5.4
H₀: μ = 5.4
<em>Alternative Hypothesis : H₁:</em> μ ≠ 5.4
Level of significance = 0.025
Test statistic
t = 1.11
<em>Degrees of freedom </em>
<em>ν = n-1 = 9-1 =8</em>
t₀.₀₁₅ , ₈ = 2.89
<em>The calculated t- value = 1.11 > 2.89 at 0.025 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4</em>
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