Contents
When to use binary random variables in statistics?
Binary Random Variables What was done in cases when looking for the mean of a distribution can also be done when sampling to determine the population parameter p for proportions. Manipulation of the standardizing formula for proportions gives:
How does sample size affect the distribution of the population?
As the sample size (n) gets larger, the sample means tend to cluster around the true population mean Holds true, regardless of the distribution of the population
What is the SD formula for sample proportion?
The distribution of the samples proportion is called a sampling distribution of sample proportions (SDSP). The SD formula is just for one sample proportion. Sampling distribution of sample means has a different SD formula.
Which is the best way to estimate a population parameter?
Generally,there are two options of estimating a population parameter. The parameter can be estimated as a single value (point estimate) and/or an interval (confidence interval estimate). The point estimate is just an average of the sample. The confidence interval, however, provides a range of values within which the true population is likely to be.
Binary Random Variables What was done in cases when looking for the mean of a distribution can also be done when sampling to determine the population parameter p for proportions. Manipulation of the standardizing formula for proportions gives: where e = (p′-p), and is the acceptable sampling error, or tolerance, for this application.
How is the acceptable error measured in a table?
The acceptable error, called tolerance in the table, is measured in plus or minus values from the actual proportion.
What is an acceptable error of 5%?
For example, an acceptable error of 5% means that if the sample proportion was found to be 26 percent, the conclusion would be that the actual population proportion is between 21 and 31 percent with a 90 percent level of confidence if a sample of 271 had been taken.
What should the sample size be for a 95 percent confidence level?
Moving from a 90 percent level of confidence to a 95 percent level at a plus or minus 5% tolerance requires changing the sample size from 271 to 384. A very common sample size often seen reported in political surveys is 384. With the survey results it is frequently stated that the results are good to a plus or minus 5% level of “accuracy”.