Scuba Diving: Depth What is the optimal amount of time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic.

The Navy defines the “optimal time” to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x 5depth of dive in meters, and let y 5optimal time in hours. A random sample of divers gave the following data (based on information taken from Medical Physiology by A. C. Guyton, M.D.).

x 14.1 24.3 30.2 38.3 51.3 20.5 22.7 y 2.58 2.08 1.58 1.03 0.75 2.38 2.20

(a) Verify that Sx 5 201.4, Sy 512.6, Sx2 5 6735.46, Sy2 5 25.607, Sxy 5 311.292, and r < 20.976.

(b) Use a 1% level of significance to test the claim that r , 0.

(c) Verify that Se < 0.1660, a < 3.366, and b < 20.0544.

(d) Find the predicted optimal time in hours for a dive depth of x 518 meters.

(e) Find an 80% confidence interval for y when x 518 meters.

(f) Use a 1% level of significance to test the claim that b , 0.

(g) Find a 90% confidence interval for b and interpret its meaning.

parts

(a) and

(b) relate to testing r. Part (c)
requests the value of Se. Parts

(d) and

(e) relate to confidence intervals for prediction. Parts

(f) and (g) relate to testing b and finding confidence intervals for b .AppendixLO1