Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 500 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes. Are researchers able to conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance using StatCrunch (directions) or calculating T and using the T-Distribution Calculator above. Based on your hypothesis test, what can we conclude?

Answer 1

Answer:

|t|  =  2.739 > 1.972 at 0.05 level of significance

Null hypothesis is rejected  at 0.05 level of significance

The researchers able to conclude from this data that the mean commute time in the U.S. is less than half an hour

Step-by-step explanation:

Step(i):-

Given sample size n = 500

Given data

mean of the sample x⁻ = 27.6 minutes

Standard deviation of the sample (S) =  19.6 minutes

Mean of the Population 'μ' = half an hour or 30 minutes

Level of significance ∝ =0.05

t₀.₀₅ = 1.972

Step(ii):-

Null hypothesis :H₀: μ= 30

Alternative Hypothesis :H₁: μ < 30

Test statistic

    $t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

   $t = \frac{27.6 -30}{\frac{19.6}{\sqrt{500} } }$

 t = - 2.739

|t| = |-2.739| = 2.739

Final answer:-

|t|  =  2.739 > 1.972 at 0.05 level of significance

Null hypothesis is rejected  at 0.05 level of significance

The researchers able to conclude from this data that the mean commute time in the U.S. is less than half an hour