statistic
QUESTION 3 (20 MARKS)
a. A psychological test identifies people as being one of eight types. For instance, Type 1 is “Rationalist” and applies to 15% of men 8 % of women. Type 2 is “Teacher” and applies to 12% of men and 14% of women. Each person fits one and only one type.
(i) Suppose college roommates have a particularly hard time getting along with each other if they are both ‘ Rationalist’. A college randomly assigns roommates of the same gender. Assuming that half of college roomate pairs are male and half are female, what proportion of all roomate pairs will both be “Rationalist”. (4 marks)
Men
Woman
Total
Rational
0.15
0.08
0,23
Teacher
0.12
0.14
0.26
Total
0.27
0.22
0.49
0.23
0.98
(ii) A psychologist has noticed that “Teachers” and “Rationalists” get along particularly well with each other, and she thinks that they tend to marry each other. One of her colleagues disagree and thinks that the types of spouses are independent of each other. If the types are independent, what is the probability that a randomly selected married couple would consist of the one “ Rationalist’ and one “Teacher”? (2 marks)
P ( T ∩ R ) = P ( T ) . P ( R )
0.26 0.23 0.26 0.23 0.49 0.49 0.49 0.49
0.26 0.49 0.26 0.49 0.49 0.23 0.49 0.23 0.26 0.26 0.23 0.23
P ( T ∩ R ) = P ( T ) . P ( R ) • • • events P ( T ) . P ( R ) are indepentdent
(iii) Refer to statment in part (ii). In surveys of thousands of randomly selected married couples, she has found that about 5% of them have one ‘Rationalist’and one ‘Teacher’.Does this contradict her colleague’s theory that the types of spouses are independent of each other? Explain
a. A psychological test identifies people as being one of eight types. For instance, Type 1 is “Rationalist” and applies to 15% of men 8 % of women. Type 2 is “Teacher” and applies to 12% of men and 14% of women. Each person fits one and only one type.
(i) Suppose college roommates have a particularly hard time getting along with each other if they are both ‘ Rationalist’. A college randomly assigns roommates of the same gender. Assuming that half of college roomate pairs are male and half are female, what proportion of all roomate pairs will both be “Rationalist”. (4 marks)
Men
Woman
Total
Rational
0.15
0.08
0,23
Teacher
0.12
0.14
0.26
Total
0.27
0.22
0.49
0.23
0.98
(ii) A psychologist has noticed that “Teachers” and “Rationalists” get along particularly well with each other, and she thinks that they tend to marry each other. One of her colleagues disagree and thinks that the types of spouses are independent of each other. If the types are independent, what is the probability that a randomly selected married couple would consist of the one “ Rationalist’ and one “Teacher”? (2 marks)
P ( T ∩ R ) = P ( T ) . P ( R )
0.26 0.23 0.26 0.23 0.49 0.49 0.49 0.49
0.26 0.49 0.26 0.49 0.49 0.23 0.49 0.23 0.26 0.26 0.23 0.23
P ( T ∩ R ) = P ( T ) . P ( R ) • • • events P ( T ) . P ( R ) are indepentdent
(iii) Refer to statment in part (ii). In surveys of thousands of randomly selected married couples, she has found that about 5% of them have one ‘Rationalist’and one ‘Teacher’.Does this contradict her colleague’s theory that the types of spouses are independent of each other? Explain