A sample of 100 students is selected from a known population of 1000 students to construct a 95% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?
To compute the standard error with a correction factor, we need to know the sample size and the population size.
In this case, the sample size is given as 100, and the population size is known to be 1000.
The correction factor, also known as the finite population correction factor, is used when the sample size is significant relative to the population size. It adjusts the standard error calculation to account for the finite population and helps in obtaining a more accurate estimate.
The formula for the correction factor is given as:
Correction Factor = sqrt[(N-n)/(N-1)]
where N is the population size and n is the sample size.
Now, plugging in the given values, we have:
Correction Factor = sqrt[(1000-100)/(1000-1)]
= sqrt[900/999]
= sqrt[0.901]
Therefore, the correction factor to compute the standard error is approximately 0.949.