Week 9 Flashcards
General z statistic
Pooled variance
When to use 2 sample tests
2 independent random samples
Hypothesise that mean of first if less than mean of second
Therefore H_0 is means are equal
Deduce z test stat for two sample test
Z stat for comparing proportions
Testing ‘no difference’ for comparison of proportions (z)
z test requires you to know
Population sd
Dist of Xbar ? Biased? Consistent?
Unbiased , consistent
Estimator for variance? Biased? Consistent?
Unbiased , consistent
Form T stat, which dist
Takes t dist w (n-1) degrees of freedom
2 sample t test? Null? Initial z?
Pooled estimator for 2 sample t test
Replace pooled estimator in z test for 2 sample t test
Place W into T test? Why? How?
Relate α % confidence interval to null hypothesis
Confidence interval is the set of value for the parameter which would not have caused us to reject the null at the (1-α)% confidence level
Denote the test stat to reject the null hypothesis μ=μ_0 at the 5% confidence level and the associated dist
Draw Z test, T test decisión tree
At what n does t dist become practically same as z
N>=60
Χ^2 test is more useful for
Categorical data
Χ^2 statistic
Where n_i is the # of observations in category I
p_i is probability of each n trial being in category i
Basically (actual - expected)^2 / expected
Expected count in each category for χ^2 test should always be
Atleast 5
Goodness of fit
To check using χ^2 wether a model (eg poussin) or categories fit
What is α for ‘Significant level’?
5%
What is α for ‘highly Significant level’?
1%
