A two sample t-test
H0 = no difference
between ideology of
parties
Ha = difference between
etc.
T= -0.46
P = 0.32
PVDA
Mean = 3.63
N = 222
St. dev = 1.21
SE of mean = 0.08
SP
Mean = 3.69
N = 249
St. dev = 1.60
SE = 0.10

** Subscribe** to view the full document.

Today’s lecture
Many studies collect data on
categorical variables
,
such as sex, nationality, political orientation, etc.
The parameters of interest in these settings are
population proportions
.
The statistic used to estimate a population
proportion is the
sample proportion
.

Sampling distribution of a sample
proportion
The sampling distribution of a sample proportion
is approximately normal (normal approximation of
a binomial distribution) when the sample size is
large enough

** Subscribe** to view the full document.

Conditions for inference on p
Assumptions:
1.
The data used for the estimate are an SRS from the population studied.
2.
The population is at least 10 times as large as the sample used for
inference. This ensures that the standard deviation of
is close to
3.
The sample size
n
is large enough that the sampling distribution can be
approximated with a normal distribution. How large a sample size is
required depends in part on the value of
p
and the test conducted.
Otherwise, rely on the binomial distribution.
1
p(
p) n.
−
p
ˆ