Question

Miami's car colorsUsing a webcam, a traffic analyst selected a random sample of $800$cars traveling on I-$195$in Miami on a weekday morning. Among the $800$cars in the sample, $24\%$were white. The margin of error for this estimate is $3.0$percentage points.

a. Would you be surprised if a census revealed that $26\%$of cars on$I-195$ in Miami on a weekday morning were white? Explain your answer.

b. Explain how the traffic analyst could decrease the margin of error.

Short answer

a. No, I would not be surprised if a census revealed that $26\%$of cars on $I-195$in Miami on a weekday morning were white.

b. Increasingthe sample size means increasing the number of cars traveling on $I-195$in Miami on a weekday morning, which will decrease the margins of error.

Step-by-step solution

Part (a) Step 1: Given Information

We are given following information:

The total number of random samples of cars is $800$.

Total number of white cars out of $800$= $\frac{24\times 800}{100}=192$

We need to explain will we be surprised if a census revealed that $26\%$of cars on $I-195$in Miami on a weekday morning were white.

Part (b) Step 2: Explanation

No, I would not be surprised if a census revealed that $26\%$of cars on$I-195$in Miami on a weekday morning were white because we expect that the parameters fall within the range of $27\%$to $21\%$.

Our data means that $26\%$of cars on$I-195$ in Miami on weekday mornings fall within our expected range.

Part (b) Step 1: Given Information

The total number of random samples of cars is $800$.

The total number of white cars out of $800$= $192$.

The margin of error for this estimate is $3.0$percentage points.

We need to explain decrease of margin due to traffic analyst.

Part (b) Step 2: Explanation

Increasing the sample size means increasing the number of cars traveling on $I-195$in Miami on a weekday morning, which will decrease the margins of error. With increasing the sample size, variability will get reduced, and we can get an accurate result.