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Math
Statistics
SCMN 5720 Minimester Exam 2 Study Guide
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Terms in this set (36)
formula for Gage R&R is
sigma(sub)e
What is the purpose of a Gage R&R Study?
Determine how much of the variation is contributed by measurement
What is the definition of Repeatability?
Variability in the measurement system within the operator's scope of influence
Reproducibility
variability in the measurement system outside of the operator's scope of influence
3 measures to assess variation are:
1. % R&R
2. %Precision to Tolerance
3. # of distinct categories
%R&R formula
Sigma(sub e)/sigma
% Precision to Tolerance formula
6*Sigma(sub)e/(USL-LSL)
What is the Kepner Tregoe approach to problem-solving?
Major objective of the analyze phase is to prove cause & effect. y=f(x's)
What is the definition of the Central Limit Theorem?
A theorem that tells us (if N is large enough),
1. The mean of the means (equal to the pop. mean)
2. The Standard Deviation of the means is S/(root)N
3. The distribution of the means is normal if N is large enough
What does the Central Limit Theorem tell us?
1. The mean of the means
2. Standard deviation of the means (S/(root)N)
3. The distribution is normal if N is large enough
Why do we use central limit theorem?
Because it proves cause and effect where X is discrete by using less data points.
Example Inferential Statistics
S(sub)r = S/(root)N
How do we calculate two-sided confidence intervals?
a= 0.05.
Formula: 1-a = 0.95, 95% confident true population mean is between two points
How do we interpret confidence intervals?
a= 0.05.
Formula: 1-a = 0.95, 95% confident true population mean is between two points
How do we find a confidence interval when sigma is known?
Use a Z-score
How do we find a confidence interval when sigma is unknown?
use a T-score (more common the Z-score)
How would we utilize confidence intervals in hypothesis testing?
...
Example from lecture - how to calc two-sided confidence interval
...
What is hypothesis testing?
A formal approach to proving cause & effect
What is the 5 step methodology for Hypothesis Testing?
1. Define null and alternative hypothesis
2. Identify Alpha
3. Calculate the Test Statistic
4. Find the critical value
5. Make decision
Define the following:
1. Define null and alternative hypothesis
2. Identify Alpha
3. Calculate the Test Statistic
4. Find the critical value
5. Make decision
1. Ho:
Ha:
2. Alpha
3. T-stat
4. Critical Value
5. Decision
How do we conduct hypothesis testing when sigma is known?
Use a Z-score
How do we conduct hypothesis testing when sigma is unknown?
...
What is the difference between a 1-sided vs. a 2-sided hypothesis test?
One-tailed has your alpha all on one side, but a two-tail disperses your alpha over 2 sides.
What is the difference between a 1 sample and 2-sample hypothesis test?
1-sample test compares one sample mean to null hypothesis calue. 2-sample test calculates difference between paired observation, then performs 1-sample t-test on the differences.
What is the p-value and how is it used?
Probability of going back into the population and getting the same results you just found if the null hypothesis is true. (Large P = indication null is true) (p<alpha, reject Ho)
What are Type I errors?
Rejecting the Null Hypothesis when it is actually true
What are Type II errors?
Failing to reject the null hypothesis when it is false
Example from 1-sample problem similar to the HW
...
What is the relationship between
1. Sample size
- Sigma
2. Type I error rate
3. Type II error rate
4. Difference we wish to detect
General Rule: If you hold any 2 of these constant, and increase the third, the fourth will decrease.
What is the purpose of scatterplots in regression analysis?
Get a good idea of the relationship between X and Y
What is the purpose of simple linear regression in regression analysis?
y=Bo+B(sub)1x
What is the purpose of interpretation of coefficients in regression analysis?
...
What is the purpose of correlation coefficients in regression analysis?
(r)
What is the purpose of the coefficient of determination in regression analysis?
(r^2)
What is the purpose of multiple regression in regression analysis?
not in Green belt body of knowledge
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