Assumptions for using (1-)100% Confidence Interval for two populations when σ is known
1) Two samples are random & independent
2) Both samples came from two independent, normal populations
3) σ_{1}^{2} (σ_{1}) and σ_{2}^{2}(σ_{2}) are known
Assumptions for using (1-)100% Confidence Interval for t-distribution
1) Two samples are random & independent
2) Both samples came from normal populations
3) σ_{1}^{2} (σ_{1}) and σ_{2}^{2}(σ_{2}) are unknown but equal
The point estimator for the unknown common variance σ^{2}^{}^{ }is
s_{p}^{2}
To test the hypothesis about unknown p_{1 }& p_{2}
we combine the information given in both samples to compute estimated variance of p_{1} & p_{2}
To construct a (1-)100% confidence interval for p_{1} and p_{2}_{ }
we do NOT combine the information contained in both samples to compute the estimated variance
A goodness of fit test
Tests the Null Hypothesis that the observed frequencies follow a pattern or theoretical distribution. The test is goodness-of-fit because the hypothesis tested is how good the observed frequencies fit a given pattern
The -squared goodness of fit test
used to test whether of not the sampled multinomial data is in agreement with the hypothesized distribution. OR Testing 3 or more unknown population proportions.
In a goodness of fit test, when is the Null Hypothesis rejected?
A good agreement between the observed and expected frequencies results in a small value of . A perfect agreement would result in =0. Thus the Null Hypothesis is rejected if is large [upper tail test]
For tests of Independence between Criterion A and B...
H_{o}: The two criteria A&B are
INDEPENDENT or not related (HoI)
For tests of Independence between Criterion A and B...
H_{A}: The two criteria A&B are
DEPENDENT or related (H_{}AD)
For tests of independence, _{} is
For tests of Independence, E_{ij}=
For a 2x2 Contingency table, testing for independence for two criteria is equivalent to testing
H_{0}: P_{1}=P_{2 }vs H_{A}:P_{1}≠P_{2}
Test of Homogeneity
A test of homogeneity involves testing the
H_{0}: the proportions of elements with certain characteristics in two or more different populations are the same