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What does standard error of proportion mean?
The standard error of a proportion is a statistic indicating how greatly a particular sample proportion is likely to differ from the proportion in the population proportion, p. Concurrently, when the normal approximation holds, sample proportion p^ is normally distributed with mean p and variance pq/n.
What is the standard error for a proportion estimate?
What is the Standard Error Formula?
| Statistic (Sample) | Formula for Standard Error. |
|---|---|
| Sample mean, | = s / √ (n) |
| Sample proportion, p | = √ [p (1-p) / n)] |
| Difference between means. | = √ [s21/n1 + s22/n2] |
| Difference between proportions. | = √ [p1(1-p1)/n1 + p2(1-p2)/n2] |
Which combination of factors will produce the largest value for the standard error?
According to the question, a small sample and a large standard deviation would produce the largest value to the standard error.
What is the largest value of standard error?
When the test is perfectly reliable, the standard error of measurement equals 0. When the test is completely unreliable, the standard error of measurement is at its maximum, equal to the standard deviation of the observed scores.
The standard error of proportion is directly proportional with sample proportion. It implies that if the sample proportion increases, then the standard error also increases and if the sample proportion decreases, then the standard error also decreases. The standard error of proportion is inversely proportional with the total number of observations.
When is the margin of error the largest?
It turns out that the margin of error is largest when p is 0.5, so we typically use this worst case estimate if no other estimate is available: We would need at least 600.25 participants, which means we need 601 participants or more, to ensure the sample proportion is within 0.04 of the true proportion with 95% confidence.
When do you need an estimate of the true proportion?
No estimate of the true proportion is required in sample size computations for a proportion, whereas an estimate of the standard deviation is always needed when computing a sample size for a margin of error for the sample mean.
Which is the null value for a single proportion?
(6.1.4) p 0 = 0.5: n p 0 = n ( 1 − p 0) = 500 × 0.5 = 250 > 10. With these conditions verified, the normal model may be applied to p ^. Next the standard error can be computed. The null value is used again here, because this is a hypothesis test for a single proportion.