Question

what is the optimal time for a scuba diver to ba on the battom of the ocean? That depan s ān the depth of the dive. The U S Navy has don a lot of research on this topic. The Navy defines the 'optimal time between length of work period and decompression time after surfacing. Letx-depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. to ba tha tima at each depth for the best balance (a) Find Tx, ty, Σ. ry2. Try, and r. (Round r to three decimal places.) c) Find a, and b. Round your answers to four decimal places.) d)Find the predicted optimal time in hours for a dive depth of x 19 meters. (Round your answer to two decimal places.) (I) Use a 1% level of significance to test the claim that βく。.(Round your answers to two decimal places.) critical - O Reject the null hypothesis. There is insufficent evidence that β Fail to reject the null hypothesis. There is insufficient evidence that p< 0. 0. 参 Fail to reject the null hypothesis. There is sufficient evidence that ß Reject the null hypothesis. There is sufficient evidence that ß 0. 0.

Answer 1

a).

$\sum x=197.40$

$\sum y=12.400$

$\sum x^{2}=6555.66$

$\sum y^{2}=24.695$

$\sum xy=299.432$

r= -0.967

b).a= 3.2042

b=-0.0508

c).for x=19 meters predicted optimum time=$[3.2042-(0.0508*19)]=2.239\sim 2.24$

d)

.$t=\frac{\hat{\beta }-\beta _{0}}{\sqrt{MSE\sum \left ( x_{i}-x \right )^2}}$

critical t= -8.51 [p value=0.000<0.01]

conclusion:

reject the null hypothesis.there is insufficient evidence that beta<0