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 response
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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