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Stat 302 Final Exam Review Study Guide Solutions Ch. 24 - ANOVA - ANSWER-ANOVA tests whether all of several populations have the same means. Only one of the sample means needs to be significantly different from another to reject the null hypothesis that all are equal. ANOVA compares the variab...

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  • November 4, 2024
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Copyright © KAYLIN 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH NOVEMBER, 2024




Stat 302 Final Exam Review Study Guide

Solutions


Ch. 24 - ANOVA - ANSWER✔✔-ANOVA tests whether all of several populations have the same means.

Only one of the sample means needs to be significantly different from another to reject the null

hypothesis that all are equal.




ANOVA compares the variability among the sample means to the variability among individuals within a

group. When the latter is too large, differences among sample means are expected to be larger just by

random chance.




Larger differences between sample means, larger sample sizes, and smaller variability in individuals

(MSE) lead to a larger F-statistic, smaller p-value, and more evidence that the population means are

different.


Ch. 4 & 23 - Regression Inference - ANSWER✔✔-At each value of x, we have a conditional distribution of

y. The regression model μ_Y=α+βx uses a straight line to approximate the relationship between x and the

mean of y at different values of x. The sample prediction equation y ̂=a+bx predicts y and estimates its

mean at the fixed value of x.




Residuals are the difference between the observed point and the line: y-(y.) ̂


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Influential points change the slope of the line substantially when added or removed. Outliers fall outside

the general pattern of the rest of the points. Outliers may or may not be influential.




Extrapolation is prediction outside of the range of observed data.




The correlation r tells us the strength of the linear relationship between x and y, and has the same sign

as the slope, which tells us the magnitude of the relationship. The p-value for the slope tells us the

significance of the slope.




The squared correlation, R2, describes the proportion of variability in y explained by x.




A hypothesis for whether slope equals 0 has hypotheses H_0:β=0 vs. H_a:β≠0,H_a:β>0,or H_a:β<0. The

test statistic for this test is t=(β-0)/se, where se is the standard error for the slope. The four assumptions

for this test can be remembered with the acronym LINE: Linear relationship, independence between

observations, normally distributed residuals, and equal variance among the errors.




A confidence interval for slope is of the form b±t_(n-2) (se), where se is the standard error of the slope.




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