For a population with a standard deviation of 10, how mlarge a sample is necessary to have a standard error that is less than or equal to 5 points?
To determine the sample size necessary to have a standard error of 5 points or less, we need to use the formula for standard error:
Standard Error = Standard Deviation / √(Sample Size)
In this case, the standard deviation is given as 10, and we want the standard error to be less than or equal to 5. Plugging these values into the formula, we can calculate the sample size.
5 = 10 / √(Sample Size)
To isolate the sample size, we can square both sides of the equation:
5^2 = (10 / √(Sample Size))^2
25 = 100 / Sample Size
Multiplying both sides by the sample size:
25 * Sample Size = 100
Dividing both sides by 25:
Sample Size = 100 / 25
Sample Size = 4
Therefore, a sample size of at least 4 is necessary to have a standard error of 5 points or less.