Question

Spend some time looking at the vehicles on the road. Look at the first 40 vehicles that drive by. Take note of the number of vehicles that are cars (sedans). Use the data you collect to construct confidence interval estimates of the proportion of vehicles that are cars (rather than trucks, vans, etc.). Report your confidence interval to the group. Why might people get different results? Is your sample likely a good representation of the total population of all vehicles? Why or why not? Make sure you show all your work and explain each of your steps to arrive at the confidence interval.

Noted as 26 sedans out of the 40 vehicle that drove by.

Please help me solve this problem. thank you.

Answer 1

ANSWER:

Given that,

Out of 40 vehicles, 26 were sedan. The sample proportion is:

              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n]

= sqrt[ 0.65 (1 - 0.65 ) / 40 ]

= 0.075415516        

Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,             

           
lower bound = p^ - z(alpha/2) * sp

= 0.65 - 1.644853627 * 0.075415516

= 0.525952515   
upper bound = p^ + z(alpha/2) * sp

=   0.65 + 1.644853627 * 0.075415516

= 0.774047485
             

Thus, the confidence interval is              
              
(   0.225952516   ,   0.474047484   )

Why might people get different results?

The amount of Sedans may be dependent on the area where the data was obtained.

Is your sample likely a good representation of the total population of all vehicles? Why or why not?

No, because I only sampled on a certain area, which most probably will not represent the total population.