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57 Cards in this Set

  • Front
  • Back
hypothesis (311)
pair of mutually exclusive, collectively exhaustive statements about the world
hypothesis testing (311)
used to test assumptions and theories and ultimately guide managers when facing decisions
H0

H1

(312)
null hypothesis (aka maintained hypothesis)

alternative hypothesis (action alternative)
facts about H0 and H1 (312)

-reject H0 or H1
-status quo
-action alternative
-we try to reject H0, even if it is favored
-H1 is referred to as the status quo
-H1 is referred to as action alternative because action may be required if we reject H0 in favor of H1
proving a null hypothesis (312)
we cannot prove a null hypothesis, but only fail to reject it. (This is how to state conclusion)
type 1 error
type 1 error probability

(313)
-rejecting the null hypothesis when it is true
-alpha
type 2 error
type 2 error probability

(313)
-failure to reject the null hypothesis when it is false
-beta
reject H0 if

true
false

(313)
type 1 error (alpha)
correct decision

convicting an innocent defendant
fail to reject Ho if

true
false

(313)
correct decision
type 2 error (beta)

fail to convict a guilty defendent
statistical hypothesis (314)
statement about the value of a population parameter that we are interested in (theta)
hypothesis test (314)
decision between two competing, mutually exclusive, and collectively exhaustive hypotheses about the value of theta
left sided test (314)
HO: theta >=Theta0
H1: theta < theta0

H0 ALWAYS has the equal sign associated with the < or > sign
two sided test 314)
H0: theta=theta0
H1: theta not equal to theta0
right tailed test 314)
HO: theta <=Theta0
H1: theta > theta0

H0 ALWAYS has the equal sign associated with the < or > sign
direction of the test indicated by H1 shows
> right tailed
< left tailed
not equal: two tailed
two tailed decision rule (316)
reject H0 if test stastitc < left tail critical value of if the test statistic> right tail critical value
left tailed decision rule (316)
reject h0 if the test statistic < left tail critical value
right tailed decision rule (316)
reject H0 if the test statistic > right tail critical vlaue
relationship between alpha and theta (319)
both alpha and beta risk can only be simultaneously reduced by increasing sample sizes
choice of alpha (319)
choice of alpha should precede the calculation of the test statistic, thereby minimizing the temptation to select alpha as to favor one conclusion over another.
testing a proportion (321)
used to test statistics that can be easily express in proportions (employee retention rates, employee accident rates
sample proportion equation (322)
p=x/n

x: number of succeses
n: sample size
z for sample proportion test (322)
equation on 322
steps for solving a hypothesis problem
1. state hypothesis
2. specify decision rule
3. calculate test statistic
4. make decision
z value for known population variance (331)
equation on 331
p value for known variance testing (333) using excel
=normdist()
z value for unknown population variance (336)
equation on 336
p value for unknown variance testing using excel (337)
=tdist()
two sample test (349)
compares two sample estimates with each other
sample proportions (351)

p1
p2
p1=x1/n1
p2=x2/n2

x= number of successes in sample
n- number of items in sample
test statistic (351)
difference of the samples proportions, p1-p2 divided by the standard error of the difference p1-p2

equation p351
pooled proportion (351)
if H0 is true, there is no difference between pi1 and pi2, so the samples can logically be pooled or averaged into one big sample to estimate the common population proportion

equation p351
comparing two means from independent samples (360)
comparing mu1 and mu2
equations for comparing two means from independent samples (360)
refer to pages 360, 361
three issues for taking means from different populations (365)

skewness/outliers
large sample sizes?
is difference important as well as significant?
with small samples, outliers, or skewed data, we may want to describe the samples rather than using the formal t comparison. outliers require consultation with a statistician.

small differences in means or proportions could be significant if the sample size is large.
paired comparison (368)
is individuals are observed twice under different circumstances.
mean of n differences (10.16)(368)
see page for equation
stdev of n differences (368)(10.17)
see page for equation
test statistic for paired samples (368)(10.18)
see page for equation

used to make the comparison
comparing two variances (374)
to see whether two variances are equal
comparing two variances equations (374)
see page
analysis of variance (393)
ANOVA- compare more than two means simultaneously

NOT THE SAME AS SIGMA

comparison of means
treatment (393)
each possible value of a factor or combination of factors
how to state ANOVA hypothesis (364)
H0=MU1=MU2=MU3=MU4
H1=not all the means are equal

if we cannot reject H0, then we conclude t hat the observations within each treatment or group actually have a common mean.
one factor ANOVA testing
only 1 variable is examined (ie location, gender, age, etc)
3 ANOVA assumptions (396)
1. observation of y are independent
2. populations being sampled are normal
3. populations being sampled have equal variances
ANOVA sample sizes (n)
equal to sum of the sample sizes for each treatment

n=n1+n2+n3...
equation of expressing the one factor ANOVA model. (397)

what is null hypothesis for Y is true
Y ij = mu+Aj+Eij

observations in treatment came from a population with a common mean plus a treatment effect plus random error

equation collapses to Yij=mu+Eij
group mean (397)
equation 11.4
overall sample mean, grand mean (397)
equation 11.5
partitioned sum of squares (397)
equations 11.6,11.7,11.8 on 398
test of two variances (399)
equation 11.9
steps of solving ANOVA problem (400)
1. state hypothesis
2. state decision rule
3. perform calculations
4. make decision
hartley's Fmax test (406)
used to compare variances of c groups.
hypotheses for hartley tests
H0=sigma1 squared =sigma2 squared=...

H1: not all the sigmaj squareds are equal
test statistic for hartley test
fmax=S^2max/S^2min
critical values for Hartley test (407)
numerator: d.f.1=c
denominator: d.f.2=(n/c) -1