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?

The degrees of freedom are given by:

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

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 ().

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the sample deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Calculate the statistic  

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

P-value  

The degrees of freedom are given by:

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

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 ().

all it means is function 3