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	14.1	24.3	28.2	38.3	51.3	20.5	22.7
y	2.58	2.28	1.58	1.03	0.75	2.38	2.20

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

Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(c) Find a, and b. (Round your answers to four decimal places.)

a =
b =

(d) Find the predicted optimal time in hours for a dive depth of x = 30 meters. (Round your answer to two decimal places.)
hr

(f) Use a 1% level of significance to test the claim that β < 0. (Round your answers to two decimal places.) Hint 1: The standard error of b is 0.007058. Hint 2: Your answers to the t and critical t should have the same sign.

t =
critical t =

Conclusion

Fail to reject the null hypothesis. There is insufficient evidence that β < 0.

Reject the null hypothesis. There is insufficient evidence that β < 0.

Fail to reject the null hypothesis. There is sufficient evidence that β < 0.

Reject the null hypothesis. There is sufficient evidence that β < 0.

Answer 1

a)