Paired Sample Tests; Inferences Concerning One Proportion - HP 50g User Manual

The criteria to use for hypothesis testing is:
Reject H if P-value <
o
Do not reject H

Paired sample tests

When we deal with two samples of size n with paired data points, instead of
testing the null hypothesis, H
deviations of the two samples, we need to treat the problem as a single sample
of the differences of the paired values. In other words, generate a new random
variable X = X -X
1
population for X. Therefore, you will need to obtain x and s for the sample of
values of x. The test should then proceed as a one-sample test using the
methods described earlier.

Inferences concerning one proportion

Suppose that we want to test the null hypothesis, H
the probability of obtaining a successful outcome in any given repetition of a
Bernoulli trial. To test the hypothesis, we perform n repetitions of the
experiment, and find that k successful outcomes are recorded. Thus, an
estimate of p is given by p' = k/n.
The variance for the sample will be estimated as s
Assume that the Z score, Z = (p-p
i.e., Z ~ N(0,1). The particular value of the statistic to test is z
Instead of using the P-value as a criterion to accept or not accept the hypothesis,
we will use the comparison between the critical value of z0 and the value of z
corresponding to
Two-tailed test
If using a two-tailed test we will find the value of z
Pr[Z> z
if P-value > .
o
:
o 1
, and test H :
2 o
0
or /2.
] = 1- (z
/2 /2
- = , using the mean values and standard
2
= , where represents the mean of the
)/s , follows the standard normal distribution,
p
) = /2, or (z
: p = p , where p represents
0 0
2
= p'(1-p')/n = k (n-k)/n
p
= (p'-p
0
, from
/2
) = 1- /2,
/2
3
.
)/s .
0 p
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