Inference for Quantitative Data
Confidence Interval for Pop. Mean
Matched pairs
Samples/experiments which treatments are carried out on the same person
T-distribution
Symmetirc/bell-shaped but have more area on its tails
Degrees of Freedom
Defines the t-distribution. (df = n – 1)
t-test: 
Constructing a Cl (use 4-step plan)
Conditions(Plan)
Independence: 10% condition when random sampling; Random assignment - what's being measured is independent
Normality: CLT (n>=30), If CLT is not met graph your sample data(note no sever skew or outlier) than assume normal
Randomness: Random sampling/Random assignment
Standard error equation: 
CI equation: 
Interpretation: We are (Confidence level) confident that the interval (Confidence Interval) captures the true mean of (context).
t-critical: invT(area = (1-CI)/2, df)
As the degress of freedom increase, the distribution approaches normal density curve
Significant Test for a Pop. Mean
Conditions
Independence: 10% condition
Normality: CLT (n>=30), If CLT is not met graph your sample data(note no sever skew or outlier) than assume normal
Randomness: Random sampling/Random assignment
Construct a 4 step plan
Plan: Check if the conditions are met
Do: t-test:
p-value = tcdf(LB, UB, df)
State: Ho/Ha
Conclude: Compare p-value and significance level to check whether H0 is rejected and do we have convincing evidence for Ha
Calculator: 1-sample t-test
Calculator: 1-sample t-int
If all conditions met, do a 1-sample t-interval
If all conditions met, use 1-sample t-test
Confidence Interval for the Diff. Of Two Means
4-step plan
Plan
Conclude
State
Do
Randomness: Random sampling/Random assignment
Independence: 10% condition for both dist.
Normality: CLT met for both n, or both dist have to have no severe skew or outliers
If all conditions met use 2-sample t-interval
Df Equation: 
Use technology to find Df
Confidence Interval Equation: 
Caculator: 2-sample t int
Define variables & your task
We are (Confidence level) confident that interval (Confidence Interval) captures the true mean difference of (context).
Significance Tests for a Diff. In Means
If 0 is included in the interval we have convincing evidence that both distribution are the same
4-Step Plan
Plan
State
Do
Define your varibales and Ho/Ha
Normality: CLT met for both n, or both dist have to have no severe skew or outliers
Independence: 10% condition for both dist.
Randomness: Random sampling/Random assignment
t-stats: 
p-value = tcdf(LB, UB, df)
If all conditions met use 2-sample t-test
Calculator: 2-sample t-test
Conclude
Compare p-value and significance level to check whether H0 is rejected and do we have convincing evidence for Ha
If its a matched pair experiment for 2 samples, we use 1-sample t-test for its significance test