Spend some time looking at the vehicles on the road Look at

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 mean number 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?

Solution

This one requires an experiment, but say you did, and found out that out of 40 cars, 14 are sedans.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.35          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    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 =   0.225952516          
upper bound = p^ + z(alpha/2) * sp =    0.474047484          
              
Thus, the confidence interval is              
              
(   0.225952516   ,   0.474047484   ) [ANSWER]

**************************

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.