Confidence Interval for μ, Standard Deviation Known (3 of 3)

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Therefore, 468.02 ≤ μ ≤ 591.98. Naturally, if a larger sample size had been used, the range of scores would have been smaller.

The computation of the 99% confidence interval is exactly the same except that 2.58 rather than 1.96 is used for z. The 99% confidence interval is: 448.54 ≤ μ ≤ 611.46. As it must be, the 99% confidence interval is even wider than the 95% confidence interval.


Summary of Computations
  1. Compute M = ΣX/N.
  2. Compute standard error of the mean
  3. Find z (1.96 for 95% interval; 2.58 for 99% interval)
  4. Lower limit = M - z σM
  5. Upper limit = M + z σM
  6. Lower limit ≤ μ ≤ Upper limit


Assumptions:
  1. Normal distribution
  2. σ is known
  3. Scores are sampled randomly and are independent



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