Question

econ 221 win13-ass 1-ECON x G Econ 221-Assign enilWinte X Get Her ework lielp With Che X Inbox 707) christop her ho123 × M Irbe 773) С https://learn.uwaterloo.ca/d21/le/content/A3261-1 161110/View iv) Generate the possible samples of n 2 individuals drawn without replacement, and for each sample find the sample mean of weekly earnings. v If simple random sampling was used to generate samples as described in iv), find the probability of the following events, a. The sample mean is at least $700 b. The sample mean is less than $1200. Question 2. You are engaged in research on smartphones sales. Are owners of home-phones (landlines) a possible market? You know from consumer surveys that 30% of households have a landline (P(L) 0.3), whereas the probability a household has a smartphone is P(S)-0.7. It isa well-established fact that P(LIS) 0.01. Answer the following, i) What is the probability that a household has both a landline and a smartphone? ii Are the events of having a landline and a smartphone statistically independent? Explain. ii What is the probability of having a smartphone given that a household has a landline? What recommendation would you make about whether or not to pursue landline owners as potential new smartphone customers?

question 2

Answer 1

I) By definition of conditional probability we have

$P(L|S) ={P(L\cap D) \over P(S)} \\ \Rightarrow P(L\cap D)=P(S) P(L|S) \\~~~~~~~~~~~~~~~~~~ =0.7\times 0.01\\~~~~~~~~~~~~~~~~~~=0.007$

II) Since

$P(S) P(L) =0.7\times 0.3=0.21\\ \Rightarrow P(L\cap D)\not=P(S) P(L)$

So S and L are not independent

III) By definition we have

$P(S|L) ={P(L\cap D)\over P(L)} ={0.007\over 0.3}\approx 0.0233$

Since probability is less Than 0.05, so it's not recommended to pursue land-line users for smart phones