Business
Statistics
Exam II
Monday February 25, 2013
7:00 pm
You will need a calculator for this exam. I will provide t tables, as well as a list of useful formulas.
I. Ethics
A. Honesty
1. don't falsify data
2. don't intentionally bias results
3. don't suppress findings
B. Data collection
1. do no harm
2. manage risks to protect subjects
3. informed consent
4. confidentiality
C. Institutional Review Board (IRB)
1. protect human subjects
2. approval required for research
II. Estimation
A. sample statistics are estimators for population parameters
1. imperfect estimates
2. random error
B. sampling errors
1. standard error
a. normally distributed
i) central limit theorem
ii) known
variance
b. calculations
i) mean
ii)
proportion
2. estimate intervals
3. increasing sample size increases
accuracy
C. confidence intervals
1. calculating interval endpoints
a. normal distribution
i) large samples, or known variance
ii) find z
values in normal table
iii)
interval = mean plus/minus z standard errors
b. t-distribution
i) small samples, estimated variance
ii) find t
values (d.f. = n-1) in
t-table
iii)
interval = mean plus/minus t standard errors
2. precision/ accuracy trade-off
D. Determining sample size
1. goal:
reach a target margin of error
2. Solve for n
a. formula for percentage
i) commonly used
ii) at worst, p =
0.5
b. formula for mean [not covered Winter 2013]
i) need to estimate standard deviation
ii) prior studies,
pilots, use likely range
E. Small populations
a. possible to sample large fraction
b. standard error is smaller
c. finite population multiplier [not covered Winter 2013]
a. formula
b. adjustment factor reduces
standard error
III. Hypothesis Testing
A. answering questions about populations based on sample results
1. base hypothesis on an idea
2. uncertainty; use probability
B. Inference
1. start
with an idea
2. specify
null and alternative hypotheses
3. specify
confidence level
4. calculate
critical region
a. built on hypothesized idea
b. standard
error
c. normal
table or t-table
5. compare
sample statistic to critical value
a. reject
null hypothesis
b. don't
reject null
6. testing
a.
two-tailed test
b. one
tailed test
C. Tests
1. mean
2. proportion
D. Comparing groups
1. difference of means
2. difference of proportions
3. test for
statistically significant differences
E. Regression
1. typical test is there a
statistically significant relation between Y and X ?
2. null hypothesis b = 0
3. use standard error of the
coefficient to construct critical region
4. reject if b is outside critical
region
5. multiple regression
6. hypothesis testing short cutsD. Significance versus Power of a test
1. Type I error
2. Type II error