Answer to Question #163880 in Statistics and Probability for ayesha

Question

The average weight of pine trees in a forest is normally distributed with mean 53.45 and

a standard deviation of 2.51. A sample of 20 pine trees are taken from the forest and their mean

is recorded 64.85. Test the hypothesis that the average weight is less than 2.51. Using Z 2.83  = .

Answer 1

Given, mean, $\mu=53.45$

standard deviation ,$\sigma=2.51$

Sample size, $n=20$

Mean of trees, $x=64.85$

The z-value is given by-

$z=\dfrac{x-\mu}\sigma$

$=\dfrac{64.85-53.45}{2.51}$

$=\dfrac{11.4}{2.51}=4.54$

Since The value of z Calculated is more than 2.51.

So Hypothesis is failed.