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- 3081 (3081)
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- Northeastern University
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Math 3081 Homework 18 .Name
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6.3.1 Commercial fishermen working certain parts of the Atlantic Ocean sometimes find their e↵orts hindered by the
presence of whales. Ideally, they would like to scare away the whales without frightening the fish. One of the
strategies being experimented with is to transmit underwater the sounds of a killer whale. On the fifty two
occasions that technique has been tried, it worked twenty-four times (that is, the whales immediately left the
area). Experience has shown, though, that 40% of all whales sighted near fishing boats leave of their own accord,
probably just to get away from the noise of the boat.
(a) Let p = P (Whale leaves area after hearing sounds of killer whale). Test H0 : p = 0.40 versus H0 : p > 0.40
at the ↵ = 0.05 level of significance. Can it be argued on the basis of these data that transmitting underwater
predator sounds is an e↵ective technique for clearing fishing waters of unwanted whales?
: 24 = 2
:
zi
52
-· 913 So no
(b) Calculate the P value for these data. For what values of a would H0 be rejected?
PV =
P (22 913).
= .
1814
6.3.2 E↵orts to find a genetic explanation for why certain people are right-handed and others left-handed have been
largely unsuccessful. Reliable data are difficult to find because of environmental factors that also influence a
child’s “handedness.” To avoid that complication, researchers often study the analogous problem of “pawedness”
in animals, where both genotypes and the environment can be partially controlled. In one such experiment (27),
mice were put into a cage having a feeding tube that was equally accessible from the right or the left. Each mouse
was then carefully watched over a number of feedings. If it used its right paw more than half the time to activate
the tube, it was defined to be “right-pawed.” Observations of this sort showed that 67% of mice belonging to strain
A/J are right-pawed. A similar protocol was followed on a sample of thirty-five mice belonging to strain A/HeJ.
Of those thirty-five, a total of eighteen were eventually classified as right-pawed. Test whether the proportion
of right-pawed mice found in the A/HeJ sample was significantly di↵erent from what was known about the A/J
strain. Use a two-sided alternative and let 0.05 be the probability associated with the critical region.
67
PLP
18 P p
:.
67 =
Ho : P :.
VS F 67
p
.
2
18 -
35.67) = 1 96
2
.
:
2 = . 05 So rej
⑳ted
67( 33)
22 - 1 96
.
if
.
.
1 96
21
.
or -
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