Question

A forester studying diameter growth of red pine believes that the mean diameter growth will be different from the known mean growth of 1.35 inches/year if a fertilization treatment is applied to the stand. He conducts his experiment, collects data from a sample of 32 plots, and gets a sample mean diameter growth of 1.6 in./year with the standard deviation of 0.46 in./year. What did the forester discovered?

Answer 1

Answer:

$t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07$  

The degrees of freedom are given by:

$df =n-1= 32-1=31$

Since is a two-sided test the p value would be:  

$p_v =2*P(t_{31}>3.07)=0.0044$  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example ($\alpha=0.01,0.05, 0.1, 0.15$).

Step-by-step explanation:

Data given and notation  

$\bar X=1.6$ represent the sample mean

$s=0.46$ represent the sample deviation

$n=32$ sample size  

$\mu_o =1.35$ represent the value that we want to test  

$\alpha$ represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

$p_v$ represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 1.35 in/year, the system of hypothesis would be:  

Null hypothesis:$\mu =1.35$  

Alternative hypothesis:$\mu \neq 1.35$  

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

$t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07$  

P-value  

The degrees of freedom are given by:

$df =n-1= 32-1=31$

Since is a two-sided test the p value would be:  

$p_v =2*P(t_{31}>3.07)=0.0044$  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example ($\alpha=0.01,0.05, 0.1, 0.15$).