In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Construct a 95% prediction interval for y, the yield, given x = 11 inches,
? = 4.379x + 4.267 and $\mathrm { Se }$ = 3.529. Round interval to two decimal places. $$\begin{array} { l | l | l | l | l | l | l | l | l | l | }
\text { Rainfall (in inches), } \mathrm { x } & 10.5 & 8.8 & 13.4 & 12.5 & 18.8 & 10.3 & 7.0 & 15.6 & 16.0 \
\hline \text { Yield (bushels per acre), } y & 50.5 & 46.2 & 58.8 & 59.0 & 82.4 & 49.2 & 31.9 & 76.0 & 78.8
\end{array}$$
A) $43.56

Question

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Construct a 95% prediction interval for y, the yield, given x = 11 inches,
? = 4.379x + 4.267 and $\mathrm { Se }$ = 3.529. Round interval to two decimal places. $$\begin{array} { l | l | l | l | l | l | l | l | l | l | } 
\text { Rainfall (in inches), } \mathrm { x } & 10.5 & 8.8 & 13.4 & 12.5 & 18.8 & 10.3 & 7.0 & 15.6 & 16.0 \
\hline \text { Yield (bushels per acre), } y & 50.5 & 46.2 & 58.8 & 59.0 & 82.4 & 49.2 & 31.9 & 76.0 & 78.8
\end{array}$$
A) $43.56 < y < 61.32$
B) $41.68 < y < 63.21$
C) $40.54 < y < 64.15$
D) $39.86 < y < 65.98$

Quizplus · Accepted Answer

To calculate the 95% prediction interval for y given x = 11 inches, we first find the predicted value of y using the given regression equation:Ŷ = 4.379(11) + 4.267 = 48.237 + 4.267 = 52.504.Then, we use the standard error of estimate (Se) to find the interval:Lower limit = Ŷ - (t*Se) = 52.504 - (1.96*3.529) = 52.504 - 6.917 = 45.587.Upper limit = Ŷ + (t*Se) = 52.504 + (1.96*3.529) = 52.504 + 6.917 = 59.421.Rounding to two decimal places, the interval is approximately $45.59 < y < 59.42$, which does not match any of the provided options exactly due to a calculation or rounding error in the question's setup or my interpretation. Given the options, A is the closest to the calculated interval, suggesting a possible mistake in my calculation or in the interpretation of the question's requirements.

In an Area of the Midwest, Records Were Kept on the Relationship