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?

Answer 1

Answer:

The confidence interval is ( 0.225952516, 0.474047484)

People will get different results because, the amount of sedans may be dependent on the area in which the data is taken.

No, the sample is not really a good representation of the whole population of vehicles, since only a certain area was sampled or experimented.

Step-by-step explanation:

Solution

Given that:

From the experiment we discovered that out of 40 vehicles, 14 of them were sedans.

Let us note that:

p^ = It is the point estimate of the population proportion

Where,

n=/n  = 0.35

We also check for the standard error of p, sp:

which is,

sp =√{p^ (1-p^)/n] =0.075415516

Thus,

for the the critical z, we have the following:

α/2 = 0.05

So,

z (α)/2 = 1.644853627

Thus,

For lower bound = p^ - z(α/2) * sp = 0.225952516

For upper bound = p^ + z(α/2)* sp = 0.474047484

Hence,

The confidence interval becomes: ( 0.225952516, 0.474047484)