STAT 503 - CHAPTER 6 EXAM QUESTIONS AND ANSWERS WITH
COMPLETE SOLUTIONS VERIFIED
sample proportion
the proportion of individuals sharing some characteristic is a population is also the
probability that an individual randomly sampled from that population will have that
attribute (a proportion can range from zero to one)
assumptions
if n is large & both np >= 5 and n(1-p) >= 5, the the random variable is approximately
normal with mean p and variance p(1-p)/n
type 1 error
if we reject H0 when H0 is true
type 2 error
if we FAIL to reject H0 when H0 is false
what affects power?
effect size, significance level, and standard error
t-test assumptions
data are simple random sample (SRS) from population; normally distributed; has the
same variance in all groups
when is it ok to ignore an assumption?
, a statistical procedure is robust to violations of an assumption if those violations have a
negligible effect on the validity of inferences (robustness usually depends on sample
size and the severity of the violation)
nonlinear transformation
may help is the response variable is strongly non-normal or sample size is too small
log transformation
applications: ratios; strong right skew; variance proportional to the mean; data spanning
several orders of magnitude
arcsine square root transformation
is a proportion (if __ is a percentage, divide it by 100) or is circular (e.g. compass
heading)
antilog (exponential) transformation
left-skew
non-parametric tests
methods include computer-intensive methods (e.g. bootstrapping) and classical, rank-
based tests
Wilcoxon signed-rank test
popular non-parametric alternative to the single-sample t-test; tests the null hypothesis
that the population median __
sign test
compares the median of a sample to a constant specified in the null hypothesis; it
makes no assumptions about the distribution of the measurement in the population
measurements lying above the null hypothesized median are designated as "+" and
COMPLETE SOLUTIONS VERIFIED
sample proportion
the proportion of individuals sharing some characteristic is a population is also the
probability that an individual randomly sampled from that population will have that
attribute (a proportion can range from zero to one)
assumptions
if n is large & both np >= 5 and n(1-p) >= 5, the the random variable is approximately
normal with mean p and variance p(1-p)/n
type 1 error
if we reject H0 when H0 is true
type 2 error
if we FAIL to reject H0 when H0 is false
what affects power?
effect size, significance level, and standard error
t-test assumptions
data are simple random sample (SRS) from population; normally distributed; has the
same variance in all groups
when is it ok to ignore an assumption?
, a statistical procedure is robust to violations of an assumption if those violations have a
negligible effect on the validity of inferences (robustness usually depends on sample
size and the severity of the violation)
nonlinear transformation
may help is the response variable is strongly non-normal or sample size is too small
log transformation
applications: ratios; strong right skew; variance proportional to the mean; data spanning
several orders of magnitude
arcsine square root transformation
is a proportion (if __ is a percentage, divide it by 100) or is circular (e.g. compass
heading)
antilog (exponential) transformation
left-skew
non-parametric tests
methods include computer-intensive methods (e.g. bootstrapping) and classical, rank-
based tests
Wilcoxon signed-rank test
popular non-parametric alternative to the single-sample t-test; tests the null hypothesis
that the population median __
sign test
compares the median of a sample to a constant specified in the null hypothesis; it
makes no assumptions about the distribution of the measurement in the population
measurements lying above the null hypothesized median are designated as "+" and
