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2026-01-17T21:15:26-08:00

99% Confidence Interval

In statistical practice the most common confidence intervals are 90%, 95%, and 99%.

For the 99% confidence interval, the Z-score is 2.58. Why? Because the central 99% of the area under a normal curve lies between Z = –2.58 and Z + 2.58.

EXAMPLE: 99% confidence interval

The following is an excerpt from an August 2011 Just the Facts publication from the Public Policy Institute for California, “Because neither of the major political parties has a majority of California’s registered voters, independents are influential in statewide elections. For example, in the previous gubernatorial election, 54% of the independents in our post-election survey said they voted for Republican Arnold Schwarzenegger. But in the 2008 presidential election, most independents (59%) said they supported Democrat Barack Obama. In each case, the outcome reflected the choice of the majority of independents.”

Suppose that the survey included 1011 randomly selected independents. Find and interpret the 99% confidence interval for the proportion of California independents who supported Barack Obama in the 2008 presidential election.

Check conditions for use of the normal model:

Conditions for use of the normal model are easily met with such a large random sample

59% of 1011 supported Obama (defined as a success) ~ 596

The rest of the 1011 did not support Obama (defined as a failure) ~ 1011 – 596 = 415

Find the confidence interval:

0.59 ± 2.58 ~ 0.59 ± 2.58 (0.015) ~ 0.59 ± 0.04

We are 99% confident that between 55% and 63% of California's independent voters supported Obama in 2008.

Confidence Interval Formula

Since we are no longer restricting our confidence level to 95%, we can generalize the formula for a confidence interval:

We use a little subscript c on the z-score, Zc , to emphasize that the z-score is connected to the confidence level. When giving the value of Zc, we always use the positive z-score.

Technology often uses 3 decimal places for Zc.

For our most common confidence levels, the values of Zc are:

90% confidence interval: Zc ≈ 1.645

95% confidence interval: Zc ≈ 1.960 (2 is a rough approximation; 1.960 is more accurate)

99% confidence interval: Zc ≈ 2.576

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