The critical value t is that value of t for which the area to its right under

The critical value t is that value of t for which the

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The critical value , t is that value of t for which the area to its right under the student’s t distribution is equal to , given degrees of freedom . Graphically, For example, suppose there are 20 degrees of freedom and we want to find the value of t such that the area to the right of it is 0.05. Locate 20 in the first column of the table and read across to the entry located in column t 0 05 . to get 1.725. Now suppose we want to find the value of t such that the area to the left of it is 0.05, given   20 . Because the t distribution is symmetric about zero, this value of t is   t 0 05 1725 . ,20 . .
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27 USING THE CHI-SQUARED TABLE OF CRITICAL VALUES The Chi-squared statistic is non-negative and its distribution is positively skewed. As with the student t distribution, the shape of the chi-squared distribution depends on the number of degrees of freedom. The critical value of   , 2 is that value of 2 for which the area to its right under the Chi- squared distribution is equal to , given degrees of freedom . Graphically, For example, suppose there are 10 degrees of freedom and we want to find the value of 2 such that the area to its right is 0.05. Locate 10 in the first column (degrees of freedom) and read across to the entry located in column 0.05 to get 18.3070. Now suppose we want to find the value of 2 such that the area to the left of it is 0.05, given   10. Because, 2 is a non-negative random variable, we must find that value of 2 such that the area to its right 0.95. Locate 10 in the first column and read across to the entry located in column 0.95 to get 3.94030.
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28 THE GREEK ALPHABET Letters Names English Equivalent Letters Names English Equivalent A Alpha A N Nu n B Beta B Xi x Gamma G O o Omicron o Delta D Pi p E Epsilon E P Rho r Z Zeta Z Sigma s H Eta - T Tau t Theta - Y Upsilon u or y I Iota I Phi - K Kappa K X Chi - Lambda L Psi - M Mu M Omega -
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29 USEFUL FORMULAE Sample Mean: n i i X n X 1 1 Sample Variance: 2 1 2 ) ( 1 1 X X n s n i i Population Variance: 2 1 2 ) ( 1 N i i X N Population Mean: N i i X N 1 1 Additive Law of Probability: P A B P A P B P A B ( ) ( ) ( ) ( ) Multiplicative Law of Probability: P A B P A B P B P B A P A ( ) ( ) ( ) ( ) ( ) Binomial Distribution: x n x x n q p C x X P ) ( E(X) = np; Var(X) = npq Standardising transformations: ) ( X Z , n X Z / ) ( , n s X t / ) ( , 2 2 2 1 s n Confidence intervals for : n z X n z X 2 2 , known n s t X n s t X n n 1 , 2 1 , 2 , unknown Confidence interval for p: n q p z p p n q p z p ˆ ˆ ˆ ˆ ˆ ˆ 2 2 , where p q ˆ 1 ˆ Confidence interval for σ 2 : 2 1 , 2 / 1 2 2 2 1 , 2 / 2 ) 1 ( ) 1 ( n n s n s n Goodness of Fit Test:
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