Assume that a random sample is used to estimate a population proportion p. find the margin of errror E that corresponds to the given statistics and confidence level
n= 550, x=165, 90%confidence
To find the margin of error (E) for estimating a population proportion (p) with a given sample size (n), number of successes in the sample (x), and a desired confidence level, follow these steps:
1. Determine the sample proportion (p-hat):
p-hat = x / n
In this case, the sample proportion is:
p-hat = 165 / 550
2. Calculate the critical value (z*) for the desired confidence level.
For a 90% confidence level, the z* value can be found using a standard normal distribution table or a statistical calculator. The z* value corresponds to the area under the standard normal curve where the cumulative probability is (1 - confidence level) / 2.
In this case, for a 90% confidence level, z* value is approximately 1.645.
3. Calculate the standard error (SE):
SE = sqrt((p-hat * (1 - p-hat)) / n)
In this case, the standard error is:
SE = sqrt((165/550) * (1 - (165/550))) / 550
4. Calculate the margin of error (E):
E = z* * SE
Substituting the values we found:
E = 1.645 * (sqrt((165/550) * (1 - (165/550))) / 550)
By following these steps, you can find the margin of error (E) for a sample size of 550, with 165 successes, and a 90% confidence level.