Testing The Difference Between Two Proportions - HP 50g User Manual

Graphing calculator.

where
(z) is the cumulative distribution function (CDF) of the standard normal
distribution (see Chapter 17).
Reject the null hypothesis, H
In other words, the rejection region is R = { |z
region is A = {|z
One-tailed test
If using a one-tailed test we will find the value of S , from
Reject the null hypothesis, H
p<p
.
0

Testing the difference between two proportions

Suppose that we want to test the null hypothesis, H
represents the probability of obtaining a successful outcome in any given
repetition of a Bernoulli trial for two populations 1 and 2. To test the
hypothesis, we perform n
find that k
successful outcomes are recorded. Also, we find k
1
outcomes out of n
respectively, by p
The variances for the samples will be estimated, respectively, as
2
s
= p
'(1-p
')/n
1
1
1
And the variance of the difference of proportions is estimated from: s
2
s
.
2
Assume that the Z score, Z = (p
distribution, i.e., Z ~ N(0,1). The particular value of the statistic to test is z
(p
'-p
'-p
)/s
.
1
2
0
p
, if z
0
| < z
}.
0
/2
Pr[Z> z ] = 1- (z ) = , or
, if z
0
repetitions of the experiment from population 1, and
1
trials in sample 2. Thus, estimates of p
2
' = k
/n
, and p
1
1
1
= k
(n
-k
)/n
1
1
1
1
-p
1
>z
, or if z
0
/2
0
| > z
0
(z ) = 1- ,
>z , and H
: p>p
0
1
' = k
/n
.
2
2
2
3
2
, and s
= p
1
2
-p
)/s
, follows the standard normal
2
0
p
< - z
.
/2
}, while the acceptance
/2
, or if z
< - z , and H
0
0
: p
-p
= p
, where the p's
0
1
2
0
successful
2
and p
1
'(1-p
')/n
= k
2
2
2
:
1
are given,
2
3
(n
-k
)/n
.
2
2
2
2
2
2
= s
+
p
1
=
0
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