Question

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. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.

x	16.1	26.3	30.2	38.3	51.3	20.5	22.7
y	2.78	2.08	1.48	1.03	0.75	2.38	2.20

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

t	=
critical t	=

Conclusion (e) Find an 80% confidence interval for y when x = 38 meters. (Round your answers to two decimal places.)

lower limit	hr
upper limit	hr

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

t	=
critical t	=

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

lower limit
upper limit

Answer 1