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Question 523:



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We'll need to compute a confidence interval around the mean to solve this one. To compute the interval we use the following steps:

  1. Find the mean and standard deviation of the 6 data-points. They are a mean of 80.45 and standard deviation of 4.976.
  2. Now we need to build the standard error around the mean (SEM) which is made up of the standard deviation divided by the square root of the sample size = 4.976/SQRT(6) = 2.0315.
  3. Next we build the margin of error, which is the SEM times a critical value from the t-distribution. We are using the t, instead of normal (or z) distribution because the sample is small and we don't know the population standard deviation. To find the critical value for 90% of the area under the t-curve we can look this value up in a t-table or use the excel function =TINV(.10,5) where the first parameter is the 1-confidence level, called alpha, and the second parameter is the degrees of freedom, or the sample size minus1. This gets us a critical value of 2.015
  4. The margin of error the SEM*t-critical value = 2.0315*2.015 =  4.093
  5. To build our interval we add and subtract the margin of error to the mean. This gets us 80.45-4.093 and 80.45+4.093 = 76.36 to 84.54.

So the 90% confidence interval is between 76.36 and 84.54 making the answer the first choice.

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