What is the optimal 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. Letx= depth of divein meters, and lety= optimal timein hours. A random sample of divers gave the following data. x= 15.1, 25.3, 32.2, 38.3, 51.3, 20.5, 22.7 y= 2.78, 2.18, 1.48, 1.03, 0.75, 2.38, 2.20

(a)(round to r to three decimal places)

x=

y=

x²=

y²=

xy=

r=

(b) Use a 1% level of significance to test the claim that< 0. (Round your answers to two decimal places.)

t=

criticalt=

(c) FindS_e,a, andb. (Round your answers to five decimal places.)

S_e=

a=

b=

(d) Find the predicted optimal time in hours for a dive depth ofx=20meters. (Round your answer to two decimal places.)

(e) Find an 80% confidence interval forywhenx=20meters. (Round your answers to two decimal places.)

lower limit=

upper limit=

(f) Use a 1% level of significance to test the claim that< 0. (Round your answers to two decimal places.)

t=

criticalt=

(g) Find a 90% confidence interval forand interpret its meaning. (Round your answers to three decimal places.)

lower limit=

upper limit=