X t s n - =
BAN CHEAT SHEET Probability Independent Event IF: Pr (AǀB) = B Confidence Intervals Eg. A 90% confidence interval estimate of the population proportion p can be interpreted to mean that if we repeatedly draw samples of the same size from the same population, 90% of the samples will result in a confidence interval that includes p. Estimating the mean when the variance is unknown: 1. 2. 3. 4.
Determine sample size (n) Calculate sample mean Calculate sample standard deviation (s) Use t-statistic
Example Simple Interpretation: We estimate that the average number of sales per year for all car salespersons is between 60.9 and 65.5 cars using a 90% confidence interval. Technical Interpretation: If we repeated the process for many random samples of 86 car salespeople then 90% of the intervals obtained would include μ in the long run. *Always show that the test statistic is valid! Hypothesis Testing Six Components of Hypothesis Testing 1. State the Hypotheses H0 : HA : 2. Test statistic
Z
t 3. 4. 5. 6.
X
n
*use if variance (or standard deviation) is KNOWN
X s
n
*use if variance (or standard deviation) is UNKNOWN
Significance level: Decision rule: Value of the test statistic Conclusion:
Determine sample size (n) Calculate sample mean Calculate sample standard deviation (s) Use t-statistic
Example Simple Interpretation: We estimate that the average number of sales per year for all car salespersons is between 60.9 and 65.5 cars using a 90% confidence interval. Technical Interpretation: If we repeated the process for many random samples of 86 car salespeople then 90% of the intervals obtained would include μ in the long run. *Always show that the test statistic is valid! Hypothesis Testing Six Components of Hypothesis Testing 1. State the Hypotheses H0 : HA : 2. Test statistic
Z
t 3. 4. 5. 6.
X
n
*use if variance (or standard deviation) is KNOWN
X s
n
*use if variance (or standard deviation) is UNKNOWN
Significance level: Decision rule: Value of the test statistic Conclusion:
