Data Analysis Notes

4483 Words Apr 26th, 2014 18 Pages
Lecture 7. Sampling Distributions.
Statistical Inference: Using statistics calculated from samples to estimate the values of population parameters. Select Random Sample Sample for (statistic) Calculate to estimate Becomes Population Parameter.
BASIC Example: Soft Drink Bottler μ=600, σ=10. Normal Distribution. What is P(X>598)? p(x<598) .
Sampling Dist.of the Mean – Distribution of all Possible Sample Means if you select a sample of a certain size. μX= μ. μ = i=1NXiN (formula for mean) . σ = i=1N(Xi-μ)2N Although you do not know how close the sample mean of any particular sample selected comes to the pop mean, you know that the mean of all possible sample means that could have been selected = the pop mean.
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OR conduct a pilot study and estimate σ with S.

Determining Sample Size for π where e =

To determine sample size for proportion you must know the desired level of confidence (1 -∝), which determines the critical Z value, The acceptable sampling error (e), and the true proportion of ‘successes’,(π) . π can be estimated with past data, a pilot sample, or conservatively use π = 0.5

In the inferential method of hypothesis testing, you consider the evidence (sample statistic) to see whether the evidence better supports the statement (null hypothesis) or the mutually exclusive alternative. Hypothesis testing is based on sample information. Methodology enables you to make inferences about a population parameter by analysing differences between the results observed (sample stat) and the results you expect to get if some underlying hypothesis is actually true. The hypothesis that assumes the status quo – that the old theory, method or standard is still true; the complement of the alternative hypothesis.
NULL HYPOTHESIS: Always contains ‘=‘ , ‘≤’ or ‘≥’ sign, May or may not be rejected, Is always about a population parameter, μ, not about a sample statistic ,Similar to the notion of innocent until proven guilty
ALTERNATE HYPOTHESIS: The hypothesis that complements the null hypothesis. Usually it is the hypothesis that the researcher is interested in proving. They are mutually exclusive and null is assumed to be true. Burden
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