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Question 858:



No answer provided yet.We need to compute the 95% confidence interval around the mean.
  1. The confidence interval is twice the margin of error and will get us our answer.
  2. The margin of error is equal to the standard error of the mean times a critical value from the t-distribution.
  3. The standard error of the mean is found as the standard deviation of the sample divided by the square root of the sample size.
So we're given the standard deviation as 40 and sample size of 25. This gets us a standard error as 40/SQRT(25) = 40/5 = 8.  Next we find the critical value from the t-distribution. We're using the t-distribution since we have a small sample size and don't know the population standard deviation. We find the critical value by looking it up in a t-table for 95% confidence on 24 degrees of freedom. We can also use the excel function =TINV(.05,24) and get the value 2.06.So we get a margin of error of 2.06*8 = 16.5.

So we can be 95% confident the actual mean time is between 93.49 minutes and 126.5 minutes. The answer to the question is then 16.5 minutes, or 16 min 30 sec.

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