What value of z should you use for a 99% confidence interval for the difference of two population proportions?

Question

BlackTom AI · Accepted Answer

To determine the z value for a 99% confidence interval for the difference of two population proportions, we need the critical z* value that corresponds to a two-tailed alpha of 0.01 (since 99% confidence leaves 1% in each tail).

Option by option analysis:

- Option 1: 2.58
  This value is the commonly used critical z* for a 99% two-sided confidence interval. Since 99% confidence implies 0.01 in each tail, the standard normal critical value that cuts off 0.005 in the upper tail of the standard normal distribution (and 0.005 in the lower tail) is approximately 2.58. This matches the standard z-table lookup for 99% confidence.

- Option 2: 2.33
  A z* of 2.33 corresponds to roughly a 98% confidence interval (two-tailed), where the total alpha is about 0.02 (0.01 in each tail). Therefore 2.33 is not appropriate for 99% confidence.

- Option 3: 3.08
  A z* around 3.08 would correspond to a much higher confidence level, well above 99%. This value is typically associated with confidence levels around 99.8% or more, depending on the exact tail probabilities, so it overstates the needed critical value for 99%.

- Option 4: 2.75
  A z* of 2.75 aligns more with a confidence level near 99.1% to 99.2% depending on the precise tail probabilities, but it is not the standard z* used for exactly 99% confidence. It is not the conventional value associated with 99%.

In summary, the 99% two-sided confidence interval requires the critical z* that leaves 0.005 in each tail, which is approximately 2.58. The other values correspond to different (lower or higher) confidence levels and do not match the 99% criterion.

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What value of z should you use for a 99% confidence interval for the difference of two population proportions?

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