You want to see if it makes a difference which lane to be in when there is traffic. You randomly observe 236 cars as they pass by on the four lane freeway. The results are displayed in the table...

You want to see if it makes a difference which lane to be in when there is traffic. You randomly observe 236 cars as they pass by on the four lane freeway. The results are displayed in the table below.  Use a level of significance of αα = 0.05.

1. Complete the rest of the table by filling in the expected frequencies:
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

   Outcome	Frequency	Expected Frequency
   Lane 1	43
   Lane 2	63
   Lane 3	79
   Lane 4	51

   
   
   
   
   
   


2. What is the correct statistical test to use?
   


3. What are the null and alternative hypotheses?
   H0:
   
   
   

   
   
   • The traffic and lanes are independent.
   
   
   • The distribution of traffic is not uniform.
   
   
   • The traffic and lanes are dependent.
   
   
   • The distribution of traffic is uniform.
   
   

   
   
   
   
   
   
   
   
   H1:
   
   
   

   
   
   • The traffic and lanes are independent.
   
   
   • The traffic and lanes are dependent.
   
   
   • The distribution of traffic is not uniform.
   
   
   • The distribution of traffic is uniform.
   
   

   
   
   
   


4. The degrees of freedom =
   
   
   
   


5. The test-statistic for this data =     (Please show your answer to three decimal places.)
   
   
   
   
   
   


6. The p-value for this sample =       (Please show your answer to four decimal places.)
   
   
   
   


7. The p-value is     α
   
   
   
   


8. Based on this, we should


9. Thus, the final conclusion is...
   
   
   

   
   
   • There is sufficient evidence to conclude that traffic and lanes are dependent.
   
   
   • There is sufficient evidence to conclude that the distribution of traffic is uniform.
   
   
   • There is sufficient evidence to conclude that the distribution of traffic is not uniform.
   
   
   • There is insufficient evidence to conclude that the distribution of traffic is not uniform.
   
   
   • There is insufficient evidence to conclude that traffic and lanes are dependent.