Answer :
This interval estimates the range in which the true proportion lies with a certain degree of confidence.
In the AP Statistics Test C - Unit V, you are working with inference for proportions. When calculating a confidence interval based on a sample of size n, follow these steps:
1. Identify the sample proportion (p-hat): Divide the number of successes (favorable outcomes) by the sample size (n).
2. Choose a confidence level (typically 90%, 95%, or 99%) which represents the probability that the true population proportion (p) lies within the calculated confidence interval.
3. Calculate the standard error (SE) of the sample proportion: SE = sqrt((p-hat)(1-p-hat)/n), where sqrt denotes the square root.
4. Determine the critical value (z*) based on the chosen confidence level. You can find this value in a standard normal (z) table or use a calculator with a built-in function for inverse normal distribution.
5. Calculate the margin of error (ME): ME = z* × SE.
6. Compute the confidence interval by adding and subtracting the margin of error from the sample proportion: (p-hat - ME, p-hat + ME).
By following these steps, you can construct a confidence interval for the population proportion based on a sample of size n. This interval estimates the range in which the true proportion lies with a certain degree of confidence.
To know more about degree of confidence, refer here:
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