The measured soil water content of n = 12 samples of soil (where 3 replicates were taken at each of 4 different depths) is given in the following table, where soil water content is measured in cubic cm of water per cubic cm of soil.
Depth (cm) Soil Water Content
10 0.313 0.299 0.340
40 0.315 0.310 0.294
60 0.289 0.284 0.281
120 0.259 0.259 0.245
a. Find a 95% CI for the slope, β1.
b. Test the hypotheses H0 :β1 = O verses HA: β1 doesn;t equal 0 at α=0.05level.
c. Construct a 95% confidence interval for μY |X=50 (i.e. the confidence band at X = 50)