Introductory statistics econ1005 | Mathematics homework help

 

 INTRODUCTORY STATISTICS ECON1005

 

Assessment 2: Problem Set #1

 

Question 1

A researcher asked 25 customers: “How much would you pay for a television adapter with Internet Access?” Their grouped responses are as follows:

 

 

Class Interval

Freq

0-99

2

100-199

2

200-249

3

250-299

3

300-349

6

350-399

3

400-499

4

500-999

2

 

 

 

a) Calculate the mean of the dataset

 

 

 

 

b) Calculate the variance of the dataset

 

Question 2

A researcher is interested in whether or not University students study for 10 hours or more a week. A sample of 100 students is taken.

 

You are given the following set of information:

 

·         the probability that a randomly selected student from a University is a female is 0.55

·         the probability that a student studies for 10 hours or more a week is 0.60

·         given that the student selected studies 10 hours or more a week, the probability that this student is male is 0.4

 

 

 

 

 

Use this information to fill in the Table below.

 

 

Studies 10 hours or

more a week

Does not study 10 hours

or more a week

 

Male

 

 

Female

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 3

 

A random sample of 80 lawyers was taken, and they were asked if they are in favour of or against capital punishment. The following table gives the two-way classification of their responses.

  

                             

                     

 

 

 

 

Favours Capital Punishment

Opposes Capital Punishment

Male

32

24

Female                    

13

11

 

 

 

 

 

 

 

           

a) If one lawyer is selected at random from this group, find the probability that this lawyer:

 

i) Opposes capital punishment given that the lawyer is a female

   

                            

                      

ii) Is a female and favours capital punishment

 

iii) Opposes capital punishment or is a male

 

b) Are the events “female” and “opposes capital punishment” mutually exclusive?

Explain why or why not.

Solution

 

c) Are the events “female” and “opposes capital punishment” independent? Explain why or why not. 

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