By: Jess Marrello
|Population (Parameter)||Sample (Statistic)|
|Z star (or critical z)||Z*|
|Degrees of Freedom||df|
|Margin of Error||ME|
|Alpha level/level of significance||α OR a|
The formulas and calculations vary because they depend on the type of test you are working with. For example, if I were asked to find the z-score, confidence interval and certain sample size for a one-sample z test, the following formulas were be the appropriate ones to use.
μ (population mean) =50
X-bar (sample mean) = 51
σ (population standard deviation) =4
n (sample size) =100
To find the z-score, you would apply this formula:
Plugging in all the given information, z = (51-50)/(4/10)=2.5
Note: The z-score is NOT the p-value. You must check the z-table in order to find the corresponding p-value.
To find the confidence interval with a 95% confidence level, you would use this formula:
Where Z* = 1.96 for 95% confidence level, which is usually given information and the 士 sign meaning that you have to add and subtract the right side of the sign to the left. This gives you two numbers, a small number and a big number, which gives you an interval. By plugging in the values, I get this interval: (50.216, 51.784).
To find the sample size, n, to obtain a margin of error of ±0.5, you would use this formula:
Where m stands for margin of error and the 0.5 is plugged into the formula without the ± symbol. If you input all the values, you should get n=((1.96×4)/(0.5))2=31.36.
For sample size you always ROUND UP to the nearest whole number even if the standard rounding rules apply. For example, my answer should be 31 according to the usual way of rounding but since we are finding sample size in this problem, my actual answer would be 32. You can’t have 0.36 of a person or a college and you cannot round down because then your sample size wouldn’t be large enough so you round up instead.
I’m Jess Marrello and I am a senior studying Exercise Science at UNM. I am hoping to become a physical therapist in the future, and am passionate about health and wellness. I love dancing, Beyonce, and breakfast!