The table lists the average gestation period (in days) and longevity (in years) for the following mammals, as reported in The World Almanac and Book of Facts 2006.   Mammal Gestation, y(days) Longevity, x(years) Mammal Gestation, y(days) Longevity, x(years) Baboon 187 20 Camel 406 12 Bear, black 219 18 Cat 63 12 Bear, grizzly 225 25 Chimpanzee 230 20 Bear, polar 240 20 Chipmunk 31 6 Beaver 105 5 Cow 284 15 Buffalo 285 15 Deer 201 8 Dog 61 12 Monkey 164 15 Donkey 365 12 Moose 240 12 Elephant 645 40 Mouse 21 3 Elk 250 15 Opossum 13 1 Fox 52 7 Pig 112 10 Giraffe 457 10 Puma 90 12 Goat 151 8 Rabbit 31 5 Gorilla 258 20 Rhinoceros 450 15 Guinea pig 48 4 Sea lion 350 12 Hippopotamus 238 41 Sheep 154 12 Horse 330 20 Squirrel 44 10 Kangaroo 36 7 Tiger 105 16 Leopard 98 12 Wolf 63 5 Lion 100 15 Zebra 365 15         Is there a linear association between mammals’ gestation and longevity?Make an accurate sketch of a scatterplot and state the correlation coefficient (r) to justify your answer.                   Use technology to find the equation for the least squares line for predicting a mammal's gestation period (y) from its longevity (x).       Use the least squares line to calculate the predicted gestation for a baboon.

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The table lists the average gestation period (in days) and longevity (in years) for the following mammals, as reported in The World Almanac and Book of Facts 2006.

 

Mammal

Gestation, y(days)

Longevity, x(years)

Mammal

Gestation, y(days)

Longevity, x(years)

Baboon

187

20

Camel

406

12

Bear, black

219

18

Cat

63

12

Bear, grizzly

225

25

Chimpanzee

230

20

Bear, polar

240

20

Chipmunk

31

6

Beaver

105

5

Cow

284

15

Buffalo

285

15

Deer

201

8

Dog

61

12

Monkey

164

15

Donkey

365

12

Moose

240

12

Elephant

645

40

Mouse

21

3

Elk

250

15

Opossum

13

1

Fox

52

7

Pig

112

10

Giraffe

457

10

Puma

90

12

Goat

151

8

Rabbit

31

5

Gorilla

258

20

Rhinoceros

450

15

Guinea pig

48

4

Sea lion

350

12

Hippopotamus

238

41

Sheep

154

12

Horse

330

20

Squirrel

44

10

Kangaroo

36

7

Tiger

105

16

Leopard

98

12

Wolf

63

5

Lion

100

15

Zebra

365

15

 

 

 

 

  1. Is there a linear association between mammals’ gestation and longevity?Make an accurate sketch of a scatterplot and state the correlation coefficient (r) to justify your answer.

 

 

 

 

 

 

 

 

 

  1. Use technology to find the equation for the least squares line for predicting a mammal's gestation period (y) from its longevity (x).

 

 

 

  1. Use the least squares line to calculate the predicted gestation for a baboon.

 

 

 

 

  1. Calculate the residual value for the gestation of a baboon, and state whether you overpredicted or underpredicted the gestation for a baboon in part (c).

 

 

 

 

 

 

  1. Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years.

 

 

 

 

  1. Why does your answer for part (e) differ so much from the average gestation period of a human (280 days)?

 

 

A biologist believes that the gestation period for a mouse is not 21 days, as reported.  She decides to randomly select 35 mice and record their gestation times, in days.  The results are given in the following table:

22

21

22

20

19

20

23

24

20

24

24

20

20

24

23

23

21

22

20

22

22

23

21

22

23

21

20

21

22

22

24

21

24

21

22

 

 

 

 

 

 

 

  1. Is there evidence to suggest that the average gestation period for a mouse is different from 21 days?Use   Be sure to complete all of the necessary steps of the hypothesis test.  No need to show work for calculations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Estimate the average gestation period of a mouse using a 95% confidence interval, and interpret your answer.
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