What is the optimal time for a scuba diver to be on the bottomof the ocean? That depends on the depth of the dive. The U.S. Navyhas done a lot of research on this topic. The Navy defines the\"optimal time\" to be the time at each depth for the best balancebetween length of work period and decompression time aftersurfacing. Let x = depth of dive in meters, and lety = optimal time in hours. A random sample of divers gavethe following data.

x	16.1	24.3	31.2	38.3	51.3	20.5	22.7
y	2.58	2.38	1.58	1.03	0.75	2.38	2.20

(a) Find Σx, Σy, Σx²,Σy², Σxy, and r. (Roundr to three decimal places.)

Σx	=
Σy	=
Σx2	=
Σy2	=
Σxy	=
r	=

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

t	=
critical t	= Â

Conclusion

Reject the null hypothesis. There is sufficient evidence thatρ < 0.Reject the null hypothesis. There is insufficientevidence that ρ < 0.    Fail toreject the null hypothesis. There is insufficient evidence thatρ < 0.Fail to reject the null hypothesis. There issufficient evidence that ρ < 0.

(c) Find S_e, a, and b. (Roundyour answers to five decimal places.)

Se	=
a	=
b	=

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

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

lower limit    Â	hr
upper limit	hr

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

t	=
critical t	=

Conclusion

Fail to reject the null hypothesis. There is insufficientevidence that β < 0.Fail to reject the null hypothesis.There is sufficient evidence that β <0.    Reject the null hypothesis. There isinsufficient evidence that β < 0.Reject the nullhypothesis. There is sufficient evidence that β <0.

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

lower limit    Â
upper limit

Interpretation

For a 1 meter increase in depth, the optimal time decreases byan amount that falls within the confidence interval.For a 1 meterincrease in depth, the optimal time decreases by an amount thatfalls outside the confidence interval.    For a1 meter increase in depth, the optimal time increases by an amountthat falls within the confidence interval.For a 1 meter increase indepth, the optimal time increases by an amount that falls outsidethe confidence interval.