Z Calculator Presentation
Leigh Anne Matthews
6/24/2016
Basic Statistics
Statistics is increasingly more relevant in the world today as more big data becomes available for analysis in fields such as Economics, Health Care, Bio-Science, Education, Psychology, Quality Control, Technology, and many others.
Standard Normal Distribuion
The Standard Normal Distribution is commonly used to standardize values “X” from a normal distribution to easily calculate the probability associated with that value, which is called the p-value.
The formula for converting a value “X” to a standardized normal z-score is:
\[ \huge z = (x-\mu) / (sd/sqrt(n)) \]
Example: Soda Can Quality Control
Quality Control wants to know if the amount of soda in each 12 oz can is correct (within 5%) or if the process needs to be fixed. The cans should contain 12 oz of soda. A sample of 100 cans has a sample mean of 11.9 oz per can and standard deviation of 0.5 oz. Are the soda cans within the acceptable limits (p-value < 0.05)?
This problem can answered by manually calculating the z-score and using hard-to-read tables, causing frustration and increasing the chances or incorrect answers… OR …You can use
The Z-Score Calculator is an R package, available for free download at https://github.com/leigh-math/Developing-Data-Products/blob/master/zcalculator.zip.
Z-Score Calculator Application
Answer: The z-score is 2 and the corresponding p-value is ~0.023, so the soda-filling process for cans is in control at the 5% level of significance.