Hypothesis Testing

4. Confidence intervals

Hypothesis Testing

The hypothesis testing problem (for the mean): make a provisional decision, based on the evidence at hand, whether a null hypothesis is true, or instead that some alternative hypothesis is true. That is, test

H ₀: E (Y) = m_{Y ,0} vs. H ₁: E (Y) > m_{Y ,0} (1-sided, >)

H ₀: E (Y) = m_{Y ,0} vs. H ₁: E (Y) < m_{Y ,0} (1-sided, <)

H ₀: E (Y) = m_{Y ,0} vs. H ₁: E (Y) ¹ m_{Y ,0} (2-sided)

Some terminology for testing statistical hypotheses:

p - value = probability of drawing a statistic (e.g. ) at least as adverse to the null as the value actually computed with your data, assuming that the null hypothesis is true.

The significance level of a test is a pre-specified probability of incorrectly rejecting the null, when the null is true.

Calculating the p-value based on :

p -value =

where is the value of actually observed (nonrandom)

Дата добавления: 2014-01-07