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Question 703:



No answer provided yet.We're given the mean of 6.44 and standard deviation of 1.89. We can compute the 95% CI using the following steps.

Part A
  1. Find the standard error of the mean (SE) which is the standard deviation divided by the square root of the sample size = 1.89/SQRT(9) = 1.89/3 = .630255.
  2. Next multiply the SE times the critical value from the t-distribution for a 95% confidence level and 8 degrees of freedom using a t-table or the Percentiles from the t-distribution calculator. We get 2.306.
  3. The margin of error is SE*tcrit = .630255 = 2.306 = 1.4533.
  4. Adding and subtracting the margin to the mean gets us a 95% CI Between 4.99 and 7.90.
Part B
The confidence interval tells us the most likely boundaries for the unknown population mean. If we were to take repeated samples from this population, we'd expect the mean to fall within this range 95% of the time.

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