1. In a study of the adsorption rate of the pesticide hexaconazole through the s

Question

1. In a study of the adsorption rate of the pesticide hexaconazole through the skin, skin specimens were exposed to 24 micrograms of hexaconazole. Four specimens were exposed for 30 minutes and four others were exposed for 60 minutes. The amounts in micrograms were 30 min 60 min 3.10 3.72 3.30 3.61 3.40 3.65 3.12 3.47 Test the hypothesis that more than 0.1 micrograms is absorbed in the time between 30 minutes and 60 minutes ( me- > 0.1 ) at= 0.05. Show and number all 5 steps of the hypothesis testing process assuming that the variances are not equal.

Explanation / Answer

Here,

Step I : Hypothesis

H0 : 1 - 2 < = 0.1 g

Ha : 1 - 2 > 0.1 g

Step II : Significance level = 0.05

Step III: Reject the null hypothesis when Test statistic t > tcritical

Here alpha = 0.05 and

degree of freedom dF = (s12 /n1 + s22 /n2)2/[(s12 /n1)2/(n1 -1) + (s22 /n2)2/(n2-1)]

Here s1 = 0.1528 ; s2 = 0.0557, n1 = n2 = 4

so degree of freedom dF = 5.4815 or 6

so tcritical = 2.015

Step 4 : Test statistic

sample mean for 30 min x1 = 3.23

Sample mean for 60 min x2 = 3.6125

standard error of mean difference se0 = sqrt [s12/n1 + s22/n2] = 0.0895

Test statistic

t = (x2 - x1 - 0.1)/ se0 = (3.6125 - 3.23 - 0.1)/ 0.0895 = 3.1572

Step V conclusion

Here t > tcritical so we will reject the null hypothesis and can conclude that there is more than 0.1 micorgrams is absoreebd inthe time between 30 and 60 minutes.

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