MATH2411_final_exam_formula_sheet

Is large enough page 2 of 6 final examination math2411

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Unformatted text preview: large enough, √ (̅ ) ( ) √ (̅ ) ( ) Page 2 of 6 Final Examination MATH2411 FORMULA SHEET AND DISTRIBUTION TABLES (c) Consider two independent random samples { are unknown. Then, (( ̅ ̅) (( ̅ )) ( } from N( ̅) √ ), and { } from N( ), where )) ( √ where where ( ) ( ( ) ( ( (II) ) ̅ (̅ √ ) ( ) confidence intervals: ̅ √ ̅) ) (̅ ( [ √ √ ̅) ) (̅ ( ) √ ̅) (III) Hypothesis Testing (critical values): √ (̅ ) √ (̅ ( ) ) √ (̅ ) √ (̅ ( | ) ) | ( √ (̅ √ (̅ ) ) ) | | OR Page 3 of 6 Final Examination (̅ ̅ MATH2411 FORMULA SHEET AND DISTRIBUTION TABLES (̅ ) ̅ √ ) | | (̅ ̅ ̅ (̅ ) √ ̅ ) | | (̅ ̅ ) | | √ √ ( | | √ √ (̅ ) ) ( ( ) OR ) ( ) (III) Hypothesis Testing (p-values): ̅ ( √ ̅ ) ̅ ̅ ( ̅ ) ) {( ( ) ( ( ( | | ) ) ) ) ̅ |) ̅ | | ̅ √ ( ̅ ) | | ) ) ( ( ( {( √ √ ( ̅ √ ( ) | | ) ̅ | ( ̅ √ ( ̅ √ ( ( ) ) √ ̅ √ ( ̅ ( ) )} ) ) ( )} Page 4 of 6 Final Examination MATH2411 FORMULA SHEET AND DISTRIBUTION TABLES (IV) Simple linear Regression Models: LS estimates : ∑ ̅)( ( ( ∑ ̅) ̅ and ̅) (∑ ∑ )(∑ (∑ ∑ ) ) ̅ ∑ MSE : ( ̅) and ∑ ∑ ∑ ̅) ( ( ̅) ̂) ( Other results : ∑ Let ( ̅) . ̂ √ √ ̂ (̅ ∑ √ √ | √ ( ) √ ∑ √ ̅) | √ ( ) √ ( | |) √ Page 5 of 6 Final Examination MATH2411 FORMULA SHEET AND DISTRIBUTION TABLES ∑ √ | ∑ √ | | ∑ √ | | ( ∑ √ ) ( ∑ √ | ) ( | ∑ √ | ) Page 6 of 6...
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