Please help! Step by step!! 5. Ecologists have been studying the relationship be
ID: 3313997 • Letter: P
Question
Please help! Step by step!!
5. Ecologists have been studying the relationship between water quality (y, on a scale from 0 to 100) and the percentage of forest in the watershed (z, in percentage points). From a sample of n = 49 watersheds. the researchers have estimated there to be a linear relationship between these two variables following the estimated regression line y 59.9 + 0.1532. The other sample quantities the researchers have calculated are: 8-17.8. sz32.2, sy18.3, x-39.4, and y = 65.9. The ecologists want a 95% estimate for the amount the water quality will improve for each additional percent of watershed forest they can protect. What is the interval estimate of interest to them? a. (-0.008, 0.314) b. (23.4, 96.7) c. (29.1, 103) d. (52.0, 68.1)Explanation / Answer
here estimated slope b1 =0.153
for std error of slope =(s/sx)*(1/(n-1))1/2 =(17.8/32.2)*(1/48)1/2 =0.0798
for 95% level and (n-2=47)degree of freedom critical value =2.0117
therefore confidence itnerval of slope =sample estimate -/+ t*Std error =0.153 -/+ 0.0798*2.0117=-0.008 ; 0.314
hence option A is cirrect