a certain type of oak tree has a mean growth of 14.3 inches in 4 years. a forest biologist believes a new variety has a greater mean growth during the same length of time. a 36 tree sample of the new variety showed a mean growth of 15.9 inches with a sample
standard deviation of 1.6 inches. can it be concluded the biologist is correct at alpha 5% or 1%

## how do i solve this problem?

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# 1 Answer

The method I use requires a graphing calculator with the t-test function. A TI-84 or TI-89 should work.

The p-value is essentially the probability that the new variety does NOT have a greater mean growth than the old variety. The answer depends on whether p<0.01; if it is, then the biologist is correct at alpha=1%. If 0.05>p>0.01, then the biologist is correct
at alpha=5%.

Because population standard deviation is unknown, use a one-sample t-test. The given information is:

*x*-bar=15.9,

*s*=1.6,

*n*=36,

*u*=14.3

_{0}From this the following can be found:

*SE*=

*s*/sqrt(

*n*) = 1.6/sqrt(36)

df =

*n*-1 = 35Use a t-test with

*x*-bar,*SE, u*and df as given or found. The appropriate test is >_{0},*u*. Find the p-value to find your answer. I get p=3.86*10^-7. This is much lower than 0.01, so the biologist is correct even at alpha=1%._{0}