HYPOTHESIS TESTING Can the observed difference be attributed

HYPOTHESIS TESTING Can the observed difference be attributed to chance? the probability that the observed difference could occur

RETAIN HO the observed mean or probability is attributed to chance when the probability of it occurring is bigger than 5% (white region) If it is just chance we stick with the status quo and RETAIN Ho.

REJECT HO the observed mean or probability is the new true value when the probability of it occurring is less than 5% (blue region). When this probability is significantly small we REJECT Ho.

Two things we test 1) probability: p-hat (a value btwn 0 and 1) 2) mean: x-bar (any value) What makes them different: Different ways to calculate the standard deviation

Two ways to test 1) 2) One tail: reject Ho if p-value smaller than alpha Two tail: reject Ho if p-value smaller than alpha/2 HA : μ ≠ a/2 Rejection region is shaded 0 Two-tail test a HA : μ > 0 Upper-tail test a HA : μ < Lower-tail test 0

Hypothesis Testing for an Observed Mean 1) State Ho and Ha 2) Check conditions: random & n<10% of population 3) Find standard deviation 4) Find z-value 5) Find p-value using z-table or normdist 6) See if your p-value is smaller than alpha 7) Reject or Retain Ho

FORMULAS TO KNOW NORMDIST(x, mean, stdv, true) gives you the p-value NORMINV (p, mean, stdv) gives you the x-value for a given p-value STANDARDIZE(x, mean, standard_dev) Gives you the z-score