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

a. Would you be surprised if a census revealed that 26%of cars onI-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

Expert verified

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

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

Step by step solution

01

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= 24800100=192

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

02

Part (b) Step 2: Explanation

No, I would not be surprised if a census revealed that 26%of cars onI-195in 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 onI-195 in Miami on weekday mornings fall within our expected range.

03

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 3.0percentage points.

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

04

Part (b) Step 2: Explanation

Increasing the sample size means increasing the number of cars traveling on I-195in 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.

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