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Question 497:



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To compute the 96% interval, we need to find the critical value using the t-distribution since we're working with the sample standard deviation and not a known population standard deviation. A 96% interval is a bit unusual and might not be in a table of values. You can use the percentile to z-score calculator and enter .96 2-sided. We get the critical value of 2.05. Now we need to compute the interval.

  1. Find the standard error of the mean (SEM) , which is the standard deviation divided by the square root of the sample size = 1.8/SQRT(64) = .225
  2. The margin of error is the SEM times the critical value we found above = .225*2.05 = .472
  3. The confidence interval is then found by adding and subtracting this from the mean. This provides us with an interval of 5.3-.472 and 5.3+.472 = 4.83 and 5.77.

So we can be 96% confident the number of days absent from school is between 4.83 and 5.77.

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