document.write( "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%. \n" ); document.write( "

Algebra.Com's Answer #782122 by Boreal(15235) $\"\"$ $\"About$

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
\n" ); document.write( "Ho: leaves are 20 or more mm in avg diameter
\n" ); document.write( "Ha: they are < 20 mm
\n" ); document.write( "alpha=0.05 P{reject Ho|Ho true}
\n" ); document.write( "test statistic is a t (0.95, df=39)
\n" ); document.write( "critical value is t<-1.66
\n" ); document.write( "t=(22-20)/1.414/sqrt(40), the variance is the sd squared, so s is sqrt (2)
\n" ); document.write( "=2*sqrt(40)/1.414=8.94
\n" ); document.write( "Again, this not surprisingly fails to reject Ho when the sample results alone are >20 mm. \n" ); document.write( "

\n" );