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handout19 - CEM 834 STATISTICS FALL 2005 IV Statistical...

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CEM 834 STATISTICS FALL 2005 IV. Statistical Examples A. Hypothesis Testing (F-test and t-test) The formation constant (K c f ) for a complex was measured by spectrophotometry (sp) and polarography (pol) with the following results: Spectrophotometry Polarography Trial K c f Trial K c f 1 98 1 104 2 109 2 101 3 105 3 95 4 120 sp x 108 pol x 100 2 sp s 84.7 2 pol s 21.0 We would like to determine if the results from these two methods are statistically equivalent. First, we need to establish whether the variances differ significantly. For this F-test, the null and alternative hypotheses are as follows: H 0 : 2 pol 2 sp s s = H a : 2 pol 2 sp s s (one-tailed F-test) The F-statistic is calculated as 03 . 4 0 . 21 7 . 84 s s F 2 pol 2 sp = = = From the tables of the F-statistic, F( α , ν 1 , ν 2 ) = F(0.05, 3, 2) = 19.16 Since the calculated F-statistic of 4.03 is less than the critical value of 19.16, we accept the null hypothesis at the 95% confidence level. Because the variances do not differ significantly, we can use the pooled variance: 2 . 59 2 n n s ) 1 n ( s ) 1 n ( s pol sp 2 pol pol 2 sp sp 2 pooled = - + - + - =
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Next, we need to establish whether the mean values differ significantly. For this t-test, the null and alternative hypotheses are as follows:
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