Statistics Final Exam Review
How many standard deviations is my hypothesis (sample mean) is away from the actual (null hypothesis population mean)
T – statistic
Rejecting the null may be a mistake = p –value
ONE SAMPLE
3 formulas
T.Dist.rt (t, sample size - 1 “df”) -> alternative that mu is bigger than a
1 – T.Dist.rt (t, sample size – 1) -> mu is less than a
T.Dist.2t(t,samplesize - 1) -> not equal to
p < significant level reject the null
NEVER accept null
TWO SAMPLE directly get the p-value chance that under the null hypthoesis, you have a difference in the sample mean that is as extreme or more as what you have now. If that probability is small, it is something in the nature not due to chance.
* Paired: T.Test (sample 1, sample 2, # of tails , 1) * not equal to: number of tails = 2 * greater than or less than: number of tails = 1 * Type 1 = paired data (ex: every UNC mba student’s salary before they entered the program and salaries after graduate ) * salaries have a significant increase after mba? * * Independent: T.Test (sample 1, sample 2, # tails, 2) * Type 2 = independent (ex: UNC mbas vs. DUKE mbas) * * * * Regression Coefficient: * * Null hypothesis: THIS regression coefficient = 0 * alternative hypothesis: THIS particular regression coefficient of interest is not 0 * * (driver’s p-value and coefficient in ANOVA) * * THIS driver’s p-value is less than significant level, then the driver has a significant impact on the outcome. * * ** for each individual driver * * * Hypothesis test on a regression model as a whole: * * Null: All slope coefficients = 0 (R square being zero) * Alt: At least ONE slope coefficient is not equal to zero (R square greater than 0) * * P-value is SIGNIFICANCE F on the ANOVA. *
IF significance F < significant level, regression model is significant as a whole. * *
T – statistic
Rejecting the null may be a mistake = p –value
ONE SAMPLE
3 formulas
T.Dist.rt (t, sample size - 1 “df”) -> alternative that mu is bigger than a
1 – T.Dist.rt (t, sample size – 1) -> mu is less than a
T.Dist.2t(t,samplesize - 1) -> not equal to
p < significant level reject the null
NEVER accept null
TWO SAMPLE directly get the p-value chance that under the null hypthoesis, you have a difference in the sample mean that is as extreme or more as what you have now. If that probability is small, it is something in the nature not due to chance.
* Paired: T.Test (sample 1, sample 2, # of tails , 1) * not equal to: number of tails = 2 * greater than or less than: number of tails = 1 * Type 1 = paired data (ex: every UNC mba student’s salary before they entered the program and salaries after graduate ) * salaries have a significant increase after mba? * * Independent: T.Test (sample 1, sample 2, # tails, 2) * Type 2 = independent (ex: UNC mbas vs. DUKE mbas) * * * * Regression Coefficient: * * Null hypothesis: THIS regression coefficient = 0 * alternative hypothesis: THIS particular regression coefficient of interest is not 0 * * (driver’s p-value and coefficient in ANOVA) * * THIS driver’s p-value is less than significant level, then the driver has a significant impact on the outcome. * * ** for each individual driver * * * Hypothesis test on a regression model as a whole: * * Null: All slope coefficients = 0 (R square being zero) * Alt: At least ONE slope coefficient is not equal to zero (R square greater than 0) * * P-value is SIGNIFICANCE F on the ANOVA. *
IF significance F < significant level, regression model is significant as a whole. * *