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.

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d