Question 1159093: Q# 3. It is hypothesized that the average diameter of the leaves of a tree is not less than 20 mm. To check this supposition a random sample of 40 leaves is selected and found that the average diameter of leaves is equal to 22 mm with variance of 2 mm. Test the hypothesis. level of significance is 5%.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! From the data, the evidence suggests that at least this sample does not have an avg diameter < 20 mm
Ho: leaves are 20 or more mm in avg diameter
Ha: they are < 20 mm
alpha=0.05 P{reject Ho|Ho true}
test statistic is a t (0.95, df=39)
critical value is t<-1.66
t=(22-20)/1.414/sqrt(40), the variance is the sd squared, so s is sqrt (2)
=2*sqrt(40)/1.414=8.94
Again, this not surprisingly fails to reject Ho when the sample results alone are >20 mm.
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