assume that a sample is used to estimate a population proportion p. find the margin of error E that corresponds to the given statistics and confidence level. 98% confidence, the sample size is 780, of which 40% are successes
what does that mean in English?
In simple terms, if you have a sample of 780 individuals and you want to estimate a population proportion with 98% confidence, where 40% of the sample are considered successes, the margin of error determines the range within which the true population proportion is likely to fall.
To calculate the margin of error, you can follow these steps:
1. Determine the sample size (n) and the sample proportion (p).
- In this case, the sample size is 780 and the sample proportion is 40% (or 0.40 as a decimal).
2. Find the critical z-value corresponding to the desired confidence level.
- For a 98% confidence level, the critical z-value is about 2.33. This value can be obtained using a standard normal distribution table or a statistical calculator.
3. Calculate the standard error (SE) using the formula:
- SE = √((p * (1 - p)) / n)
- SE represents the variability of the sample proportion around the true population proportion.
4. Compute the margin of error (E):
- E = z * SE
- Multiply the critical z-value by the standard error.
By applying these steps, you can find the margin of error that corresponds to the given statistics and confidence level.