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10.5 Liver alcohol dehydrogenase activity in two random samples of catfish was determined One sample was taken upstream from a brew ery, and the other sample was taken down stream from the brewery. We wish to know if living downstream from a brewery increases liver alcohol dehydrogenase in these animals. The results were as follows. Upstream Downstream 10 25 30 32 28 35 29 32 32 38 31 19 30

math   Statistics-And-Probability   
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First we need to find the descriptive statistics of data. Following is the output of descriptive statistics generated by excel:

Descriptive statistics count mean sample standard deviation sample variance minimum maximum range Upstream, X1 8 14.38 9.20 84.55 Downstream, X2 9 31.89 18» 3.06 9.36 28 38 10 30 25

Here we have ή -14.38,5, 9.2,n, 8 31.89,s, -3.06, n,9 Hypotheses are Test is left tailed. Level of significance: α-0.05 Since we cannot assume that variances are equal so degree of freedom of t test will be i ni df Test Statistics: ((14.38-31.89)-0)/(sqrt(84.64/8)+(9.3636/9))) -5.137 1 n2 Critical value: CV =-1.833 Rejection Region: If t <-1.833, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value: P-value-0.0003 Decision: Since p-value is less than level of significance so we reject the null hypothesis Excel function for critical value: ะโ1NV(0.19) =TDIST(5.137,91) Excel function for p-value:

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