A researcher from the crop and soil sciences department at your local university is interested in the relationship between the amount of phosphorus and nitrogen found in the ground. She takes a random sample of sites in the Commonwealth of Virginia and fits a linear regression model to the data. Based on this model, she obtains the following prediction results:
$$\begin{array} { | c | c | c | c | c | }
\hline \text { Nitrogen Level } & \begin{array} { c }
\text { Predicted } \
\text { Phosphorus Level }
\end{array} & \begin{array} { c }
\text { Std Error } \
\text { Predict }
\end{array} & \mathbf { 9 5 . 0 \% } \text { CI } & \mathbf { 9 5 . 0 \% } \text { PI } \
\hline 20 & 15 & 1.25 & ( 12,18 ) & ( 10,20 ) \
\hline
\end{array}$$ What is a 95% confidence interval for the mean amount of phosphorus when the nitrogen level is 20?

Question

A researcher from the crop and soil sciences department at your local university is interested in the relationship between the amount of phosphorus and nitrogen found in the ground. She takes a random sample of sites in the Commonwealth of Virginia and fits a linear regression model to the data. Based on this model, she obtains the following prediction results:
$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Nitrogen Level } & \begin{array} { c } 
\text { Predicted } \
\text { Phosphorus Level }
\end{array} & \begin{array} { c } 
\text { Std Error } \
\text { Predict }
\end{array} & \mathbf { 9 5 . 0 \% } \text { CI } & \mathbf { 9 5 . 0 \% } \text { PI } \
\hline 20 & 15 & 1.25 & ( 12,18 ) & ( 10,20 ) \
\hline
\end{array}$$ What is a 95% confidence interval for the mean amount of phosphorus when the nitrogen level is 20?

Quizplus · Accepted Answer

The 95% confidence interval for the mean amount of phosphorus when the nitrogen level is 20 is given directly in the table as (12, 18). This interval estimates the average phosphorus level for all sites with a nitrogen level of 20.

A Researcher from the Crop and Soil Sciences Department at Your