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 cuts
    7.  R-squared
        a. coefficient of determination
        b. low R-squared-- lots of unexplained variation in Y

D. Significance versus Power of a test

    1. Type I error
    2. Type II error


 



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