The police chief of a town is trying to determine the average speed of the drivers on a specific road. The police chief took a random sample of speeds of 100 drivers on the road.The mean was 48.5 miles per hour, with a standard deviation of 2.5 miles per hour.The police chief wanted to decrease the margin of error of his next sample.Which choice would decrease the margin of error?Note: Margin of error = 2(sn√)2(𝑠𝑛), where s is the standard deviation and n is the sample size.
Question
The police chief of a town is trying to determine the average speed of the drivers on a specific road. The police chief took a random sample of speeds of 100 drivers on the road.The mean was 48.5 miles per hour, with a standard deviation of 2.5 miles per hour.The police chief wanted to decrease the margin of error of his next sample.Which choice would decrease the margin of error?Note: Margin of error = 2(sn√)2(𝑠𝑛), where s is the standard deviation and n is the sample size.
Solution
The margin of error can be decreased in two ways: either by decreasing the standard deviation (s) or by increasing the sample size (n). In this case, the police chief cannot control the standard deviation as it is a measure of the variability of the drivers' speeds. However, he can control the sample size. Therefore, to decrease the margin of error, the police chief should increase the sample size for his next sample.
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