Question

Obedience School for Dogs is a small franchise that offers obedience classes for dogs. Some people think that larger dogs are easier to train and, therefore, should not be charged as much for the classes. To investigate this claim, dogs enrolled in the classes were classified as large (?? pounds or more) or small (under ?? pounds). The dogs were also classified by whether or not they passed the obedience class offered by the franchise. ??% of the dogs involved in the classes were large. ??% of the dogs passed the class. Records indicate that ??% of the dogs in the classes were small and passed the course.

1) Copy and Complete the following hypothetical 1000 two-way table: Passed the Course Did Not Pass the Course Total Large Dogs Small Dogs Total 2) Estimate the probability that a dog selected at random from those enrolled in the classes passed the course. 3) A dog was randomly selected from the dogs that completed the class. If the selected dog was a large dog, what is the probability this dog passed the course? 4) A dog was randomly selected from the dogs that completed the class. If the selected dog is a small dog, what is the probability this dog passed the course? 5) Do you think dog size and whether or not a dog passes the course are related? 6) Do you think large dogs should get a discount. Explain your answer.

Answer 1

Answer:-

Given That:-

Obedience School for Dogs is a small franchise that offers obedience classes for dogs. Some people think that larger dogs are easier to train and, therefore, should not be charged as much for the classes. To investigate this claim, dogs enrolled in the classes were classified as large (?? pounds or more) or small (under ?? pounds). The dogs were also classified by whether or not they passed the obedience class offered by the franchise. ??% of the dogs involved in the classes were large. ??% of the dogs passed the class. Records indicate that ??% of the dogs in the classes were small and passed the course.

L = IT's a large dog

PC = the dog passed the course

S = It's a small dog

P (L) = 45\100

= 0.45

P (L) = 0.45

P (PC) = 60/100

= 0.6

P (PC) = 0.6

P (S) = P (L^C) = 1 - 0.45

= 0.55

P (S) = 0.55

= 0.4

= 0.55 - 0.4

= 0.15

= 0.6 - 0.4

= 0.2

= 0.55 + 0.6 - 0.4

= 0.75

= 1 - 0.75

= 0.25

1) Copy and Complete the following hypothetical 1000 two-way table:

	Passed the Course (PC)	Did not pass the course P(PCC)	Total
Large Dogs (SC/L)	1000 0.2 = 200	1000 0.25 = 250	450
Small Dogs (S)	1000 0.4 = 400	1000 0.15 = 150	550
Total	600	400	1000

2) Estimate the probability that a dog selected at random from those enrolled in the classes passed the course.

P (randomly selected dog enrolled in the classes passed the course)

P (PC) = 0.6

or

P (randomly select dog enrolled in the classes passed the course)

[we can choose 1 dog from 600 dogs who passed the course]

[we can choose 1 dog from total no. of dogs]

= 600 / 1000

= 0.6

3) A dog was randomly selected from the dogs that completed the class. If the selected dog was a large dog, what is the probability this dog passed the course?

P (randomly selected dog passed the course \ dog is large dog)

= P(PC / S^C)

= 0.444

4) A dog was randomly selected from the dogs that completed the class. If the selected dog is a small dog, what is the probability this dog passed the course?

P (randomly selected dog passed the course / dog is small)

= P (PC / S)

= 0.707

5) Do you think dog size and whether or not a dog passes the course are related?

Take

Therefore size of the dog & whether the dog passes the course are not independent i.e, they are related.

6) Do you think large dogs should get a discount. Explain your answer.

Large dogs should not get a discount as we can see probability of large dogs passing the tests is smaller than large dogs passing the tests.

So, It's not true that larger dogs are easier to train rather we can say smaller dogs are easier to train.

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