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  1. Prepare
  2. Artificial Intelligence
  3. Probability & Statistics - Foundations
  4. The Central Limit Theorem #4
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The Central Limit Theorem #4

  • MrStubby007
     + 0 comments

    Here are the steps to find the confidence interval(CI):

    1. Select Confidence level(CL): 95%(given)

    2. Calculate Margin of Error(ME):

      Follow below steps -

      • Find Standard Error(SE)

        SE = σ/sqrt(n) = 80/10 = 8

      • Find Critical Value:

        1. Calculate alpha(α)

          α = 1-CL/100 = 1-0.95 = 0.05

        2. Calculate Critical Probability(p*)

          p* = 1-α/2 = 1-0.025 = 0.975

        3. Compute degree of freedom(df)

          df = n-1 = 100-1 = 99

          Therefore, critical value is t-statistics having 99 df and cumulative prob. equals to 0.975 Or, We can also expressed the critical value as a z-score since the
          sample size is large, so a z-score analysis produces the same
          result.

          critical value = 1.96.

      ME = critical value * SE In our case, ME = 1.96*8

    3. The range of the confidence interval is (sample statistic - margin of error, sample statistic + margin of error)

      In our case, CI = (500-1.96*8, 500+1.96*8)

      or, CI = (484.32, 515.68)