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Question 485:



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We will want to generate the standard error of the mean around the observed sample mean of 100cm. The standard error of the mean is made up of the standard deviation divided by the square root of the sample size.

  1. SEM: s/SQRT(n) = 60/SQRT(900) = 60/30 = 2, or 1 standard error is 2 cm, which is the sampling distribution or the standard deviation of the sample mean.
  2. To construct the 99% confidence interval we need to multiply the SEM times a critical value from the t or normal distribution. Since this sample is large (900) there won't be much difference. I'll use the t-distribution critical value as it will provide a slightly more conservative interval. To find the critical value we can use the Excel formula =TINV(.01, 899) where the parameters are the 1- confidence level (called alpha) and the degrees of freedom or 1 less than the sample size.  We get the critical value of 2.581 (the normal deviate would be 2.575 or very little difference).
  3. We now want the margin of error which is the critical value we just found times the SEM = 2.58*2 = a margin of error of 5.16.
  4. The confidence interval is just the mean plus or minus this margin of error so the 99% confidence interval is 100-5.16 and 100+5.16 = an interval between (94.84 and 105.16)

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