Cicadas are flying, plant-eating insects. One particular species, the 13-year cicadas (Magicicada), spemds five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams, and wing lengths (WL) in millimeters, are given for three different species of these 13-year cicadas in the following table:
BW WL Species BW WL Species
0.15 28 tredecula 0.18 29 tredecula
0.29 32 tredecim 0.21 27 tredecassini
0.17 27 tredecim 0.15 30 tredecula
0.18 30 tredecula 0.17 27 tredecula
0.39 35 tredecim 0.13 27 tredecassini
0.26 31 tredecim 0.17 29 tredecassini
0.17 29 tredecassini 0.23 30 tredecassini
0.16 28 tredecassini 0.12 22 tredecim
0.14 25 tredecassini 0.26 30 tredecula
0.14 28 tredecassini 0.19 30 tredecula
0.28 25 tredecassini 0.2 30 tredecassini
0.12 28 tredecim 0.14 23 tredecula
a. Draw a scatter diagram with body weight as the independent variable and wing length as the dependent variable. Find the equation of the line of best fit.
b. Is body weight an effective predictor of wing length for a 13-year old cicada? Use a 0.05 level of significance.
c. Give a 90% confidence interval for the mean wing length for all 0.20 gram cicada body weight.