A farmer is curious how fertilizer influences the yield of wheat. To study this

Question

A farmer is curious how fertilizer influences the yield of wheat. To study this effect, he dedicates several test acres and measures the yield of wheat (in bushels per acre) and records the amount of fertilizer applied to that acre (in pounds per acre). From his measurements on n = 7 acres, he estimates there to be a linear relationship between these two variables following the estimated regression line y = 11.33 + 0.07x. He has also calculated the following: ˆy = 35.9, s = 3.62, sx = 79.6, sy = 6.48, ¯x = 642, and ¯y = 56.3. The farmer wants an 95% estimate for the average increase in wheat yield for each additional pound of fertilizer applied. What is the interval of interest to him? a. (0.02, 0.12) b. (18.8, 53.0) c. (21.6, 50.2) d. (26.6, 45.2)

Explanation / Answer

For 95% confidence interval ,degree of freedom error=n-2=7-2=5 and critical t=2.571

Prediction yhat=35.9

95% confience interval =yhat± t(0.05,139)*se*sqrt(1/n+(x0-xbar)2/(n-1)sx2)

=35.9 ±2.571 *3.62*sqrt(1/7+(351-642)2/(7-1)*79.62)

=(21.57            50.23)

So part-c is answer

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