Transcript Review of Hypothesis Testing

Review of Hypothesis Testing
Types of Tests
1) 1-Sample z
2) 1-Sample t
3) 2-Sample t
4) 1-Proportion
5) 2-Proportion
6) Paired t-test
7) Chi-Square G.O.F test
8) Chi-Square Test of Independence
9) Linear Regression t-test
Universal Conditions
1. Randomization Condition: The sample should
be a simple random sample of the population.
2. 10% Condition: (Independence) If sampling has
not been made with replacement, and you are
drawing from a finite population then the
sample size, n, must be no larger than 10% of
the population.
1-Sample-Z Test
• Quantitative Data
• You know (sigma) the standard deviation of
the population.
• Normality Check: Stated in the question,
probability plot, n is at least 30.
1-Sample t-test
• Quantitative Data
• You do not know (sigma) the standard deviation
of the population.
• You use “s” the standard deviation of the
sample to approximate sigma.
• Normality Check: (Central Limit Theorem)
Sample Size of at least 30
2-Sample t-test
• 2 Sets of Quantitative Data
• You do not know (sigma) the standard
deviation of either population.
• You use s1 and s2 to approximate sigma for
both populations.
• Normality Check: (CLT) Both sample sizes are
at least 30.
1-Proportion
• (Categorical Data) Qualitative Data
• You use p-hat and q-hat to approximate the
standard deviation of the population.
pq
n
• Normality Check: The sample size has to be
big enough so that both np and nq are at
least 10.
2-Proportion
• 2 Sets of (Categorical Data) Qualitative Data
• You use p-hat and q-hat to approximate the
standard deviation for both populations.
p1q1
n1
p2 q2
n2
• Success/Failure Condition: The sample size has
to be big enough so that both n1p1, n1q1
n2p2, n2p2 are at least 10.
Paired t-test
• Quantitative Data
• Same as a one sample t-test but you have two
pieces of data for each subject or experimental
unit.
• Usually (Pre-Test/Post-Test)
• Normality Check: (CLT) “n” is at least 30
Chi-Square Goodness of Fit
• When you are comparing multiple proportions
for a distribution. (M & M project)
• Conditions:
• No expected counts less than 5.
• All variables are independent.
Expected Counts equal sample size multiplied by
the %’s stated in the model.
Chi-Square Test of Independence
• When you are comparing two categorical
variables. (Two Way Table)
• Conditions:
• No expected counts less than 5.
• All values are independent.
Finding Expected Counts
The expected count in any cell of a two-way table when H0 is true is
row total  column total
expected count =
table total
Linear Regression t-test
Conditions for Regression Inference
Suppose we have n observations on an explanatory variable x and a
response variable y. Our goal is to study or predict the behavior of y for
given values of x.
• Linear The (true) relationship between x and y is linear. For any fixed
value of x, the mean response µy falls on the population (true) regression
line µy= α + βx. The slope b and intercept a are usually unknown
parameters.
• Independent Individual observations are independent of each other.
• Normal For any fixed value of x, the response y varies according to a
Normal distribution.
• Equal variance The standard deviation of y (call it σ) is the same for all
values of x. The common standard deviation σ is usually an unknown
parameter.
• Random The data come from a well-designed random sample or
randomized experiment.