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Answer:
<em>|t| = 2.739 > 1.972 at 0.05 level of significance</em>
<em>Null hypothesis is rejected at 0.05 level of significance</em>
<em>The researchers able to conclude from this data that the mean commute time in the U.S. is less than half an hour</em>
<u>Step-by-step explanation</u>:
<u>Step(i)</u>:-
Given sample size n = 500
Given data
<em>mean of the sample x⁻ = 27.6 minutes</em>
<em>Standard deviation of the sample (S) = 19.6 minutes</em>
<em>Mean of the Population 'μ' = half an hour or 30 minutes</em>
<em>Level of significance ∝ =0.05</em>
t₀.₀₅ = 1.972
<u><em>Step(ii):</em></u>-
<u><em>Null hypothesis :H₀</em></u>: <em>μ= 30</em>
<u><em>Alternative Hypothesis :H₁:</em></u> <em>μ < 30</em>
Test statistic
t = - 2.739
|t| = |-2.739| = 2.739
<u><em>Final answer</em></u>:-
<em>|t| = 2.739 > 1.972 at 0.05 level of significance</em>
<em>Null hypothesis is rejected at 0.05 level of significance</em>
<em>The researchers able to conclude from this data that the mean commute time in the U.S. is less than half an hour</em>
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