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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