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The following interval calculations for the proportion
confidence interval is dependent on the following assumptions being
satisfied: Np ≥ 10 and n(1 - p) ≥ 10. If p is unknown then use the sample proportion.

The goal is to estimate p = proportion with a particular trait or opinion in a population.

Sample statistic = p^ (read "p-hat") = proportion of observed sample with the trait or opinion we’re studying.

Standard error p^=p^(1−p^)n−−−−−√, where n = sample size.

Multiplier comes from this table (a subset of the standard normal table)

Confidence level and corresponding multiplier.

Confidence Level

Multiplier

.90 (90%)

1.645 or 1.65

.95 (95%)

1.96, usually rounded to 2

.98 (98%)

2.33

.99 (99%)

2.58

The value of the multiplier increases as the confidence level increases. This leads to wider intervals for higher confidence levels. We are more confident of catching the population value when we use a wider interval.

Please let me know if you need any clarification. I'm always happy to answer your questions.