Assume that all grade-point averages are to be standardized on a scale between 0 and 6. how manygrade-point averages must be obtained so that the sample mean is within 0.006 of the population mean? assume that a 99% confidence level is desired. if using the range rule ofthumb, σ can be estimated as range/4=6-0/4 = 1.5. does the sample size seempractical?
416025 grade-point averages must be obtained so that the sample mean is within 0.006 of the population mean. But this size too big and is not practical.
Minimum required grade-point averages can be found using the formula
N≥ whereN is the sample sizez is the corresponding z-score in 99% confidence level (2.58)s is the standard deviation (1.5)ME is the margin of error (0.006)
Putting these numbers in the formula we get