The highway safety department wants to study the driving habits of individuals. a sample of 32 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. what sample size should be chosen if we want a margin of error of less than 2 miles per hour for a 95% confidence interval?

n=126

Step-by-step explanation:

Data given and previous concepts

represent the sample mean

represent the sample deviation

n=32 represent the sample size

Confidence =0.95 or 95%

represent the significance level

ME= 2 represent the margin of error required

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

Solution to the problem

Since we don't have the population deviation. We know that the margin of error for a confidence interval is given by:

  (1)

The next step would be find the value of , and . The degrees of freedom are given by:

Using the normal standard table, excel or a calculator we see that:

And the code in excel is this one:  "=T.INV(1-0.025,31)"

If we solve for n from formula (1) we got:

And we have everything to replace into the formula:

And if we round up the answer we see that the value of n to ensure the margin of error required is n=126.

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