Answer:
<em>The calculated value z = 1.3145 < 2.326 at 0.02 level of significance</em>
<em>The null hypothesis is accepted </em>
<em>Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.</em>
Step-by-step explanation:
<em><u>Step(i)</u></em>:-
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
<em>The mean of the Population 'μ' = 28.0miles/gallon</em>
Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.
<em>The sample size 'n' = 270 </em>
<em>Mean of the sample 'x⁻' = 27.8</em>
<em>Given Population variance 'σ² = 6.25</em>
<em>The standard deviation of Population 'σ' = √6.25 = 2.5</em>
<u><em>Step(ii):-</em></u>
<em>Null hypothesis :H₀: 'μ' = 28.</em>
<em>Alternative hypothesis :H₁: 'μ' ≠28.</em>
<em>The test statistic </em>
<em></em><em></em>
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<em>Z = -1.3145</em>
|Z| = |<em>-1.3145|= 1.3145</em>
<u><em>Step(iii)</em></u><em>:-</em>
<em>The tabulated value of z-score at 0.02 level of significance = 2.326</em>
The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance
<em>The null hypothesis is accepted </em>
<em>Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.</em>
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