一、sampling variability & CLT for proportions
if the success-failure condition is notmet:
‣ the center of the sampling distributionwill still be around the true population proportion
‣ the spread of the sampling distributioncan still be approximated using the same formula for the standard error
‣ the shape of the distribution willdepend on whether the true population proportion is closer to 0 or closer to 1
二、confidence interval for a proportion
三、hypothesis test for a proportion
四、estimating the difference between two proportions
五、hypothesis tests for comparing two proportions
六、small sample proportion
七、chi-square GOF test
evaluating the hypotheses
‣ quantify how different the observedcounts are from the expected counts
‣ large deviations from what would beexpected based on sampling variation (chance) alone provide strong evidence forthe alternative hypothesis
‣ called a goodness of fit test sincewe’re evaluating how well the observed data fit the expected distribution
p-value
‣ p-value for a chi-square test is definedas the tail area above the calculated test statistic
‣ because the test statistic is alwayspositive, and a higher test statistic means a higher deviation from the nullhypothesis
八、chi-square independence test
evaluating the hypotheses
‣ quantify how different the observedcounts are from the expected counts
‣ large deviations from what would beexpected based on sampling variation (chance) alone provide strong evidence forthe alternative hypothesis
‣ called an independence test since we’reevaluating the relationship between two categorical variables
chi-square tests
‣ goodness of fit: comparing thedistribution of one categorical variable (with more than 2 levels) to ahypothesized distribution
‣ independence: evaluating therelationship between two categorical variables (at least one with more than 2levels)