Question

A smallsample ofUWIstudents were asked whethertheywere in favor of or against abortion. Some information about these students is shownbelow.

student surveyed	sex	age	abortion option	religious identity number of children
1	f	24	in favor	agnostic 0
2	m	22	in favor	non denominational church 1
3	f	41	against	catholic 5
4	m	38	against	evangelical 4
5	f	18	in favor	catholic 0
6	m	19	against	atheist

a. how many elements are in the data set?

b. How many variables are in the data set

c. which of the variables are categorical and which are quantitative

2 Asurvey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.

a. What is the probability of selectingan individual who is majoringinMarketing?

b. What is the probability of selecting a female?

c. Whatistheprobability ofselecting a femalewhoisalsomajoring in Management?

d. Whatistheprobabilityofselectinganindividualwhoismajoring in Management, given that the person isfemale?

e. What is the probability of selecting a female OR a management Major.

f. Are the events “Female” and “Management ” mutually exclusive? Explain using probabilities

g. Are the events “Female” and “Management ” independent events? Explain using probabilities.

gender	management	marketing	others	total
male	40	10	30	80
female	30	20	70	120
total	70	30	100	200

Answer 1

Solution-

Considering the information in the table regarding sample of UWI students of whethertheywere in favor of or against abortion.

(a)

Elements in the data set are the number of members in that sample.

So, here number elements in the data set are 6.

(b)

There are 5 variables in the data set namely sex, age, abortion option , religious identity and number of children.

(c)

The variables are said to categorical if they can not be counted and variable are said to be quantitative if they are countable.

Here,

Categorial variables are sex, religious identity.

And

Quantitative variables are age, abortion option and number of childrens.

(2)

Considering the survey of a sample of business students regarding the genders of the individuals and their selected major.

Gender	Management	Marketing	Others	Total
Male	40	10	30	80
Female	30	20	70	120
Total	70	30	100	200

Now,

(a)

The probability of selecting an individual who is majoring in Marketing

=(Total students major in marketing)/(Total students surveyed)

=30/200

=0.15

(b)

The probability of selecting a female

=(Total females surveyed)/(Total students surveyed)

=120/200

=0.60

(c)

The probability of selecting a female who is also majoring in Management

=(Number of females majoring in management)/(Total students surveyed)

=30/200

=0.15

(d)

The probability of selecting an individual who is majoring in Management given that the person is female

=(Number of females who are majoring in management)/(Total females surveyed)

=30/120

=0.25

(e)

The probability of selecting a female OR a management Major

=(Number of females surveyed +number of males who are also majoring in management)/(Total students surveyed)

=(120 +40)/200

=(160)/200

= 0.80

(f).

The events “Female” and “Management ” mutually exclusive if

P(Female or Management) = P(Female) + P(Management)

Now,

=P(Female or management)

=(120 +40)/200 = 160/200

= 0.80 .....(1)

P(Female) +P(Management)

= 120/200 +70/200

= 0.60 + 0.35

= 0.95 ...(2)

From equations (1) and (2), we get

P(Female or Management) ≠ P(Female) +P(Management)

Hence, P(Female and Manangement) are not mutually exclusive.

(g)

The events “Female” and “Management ” independent events is

P(Female and Management )=P(Female)×P(Management)

Now,

P(female and Management)

=30/200 = 0.15

P(Female)×P(Management)

= (120/200)×(70/200) = 0.6×0.35 = 0.21

Since

P(Female and Maangement ) ≠ P(Female)×P(Mangement)

Hence, Probability of Female and Management is is not independent.