How will marketers change their social media use in the near future? A survey by Social Media Examiner reported that 76% of B2B marketers (marketers that focus primarily on attracting businesses) plan to increase their use of LinkedIn, as compared to 52% of B2C marketers (marketers that primarily target consumers). The survey was based on 1,780 B2B marketers and 3,306 B2C marketers (let’s assume the survey data are the population). The following table summarizes the results:
Business focus
Increase use of LinkedIn? B2B B2C Total
Yes 1,353 1,719 3,072
No 427 1,587 2,014
Total 1,780 3,306 5,086
(e) If 10 marketers out of 5,086 survey respondents were selected at random as a sample, what
is the probability that 7 B2B marketers are included in the same? (use the binomial
distribution with the parameter ? from the survey data)
(f) If 200 marketers out of 5,086 survey respondents were selected
at random as a sample, what
is the probability that the proportion of B2B marketers in the sample is between 100 and 140 (i.e., 50 to 70%)? (use the normal distribution based on the central limit theorem)
e)
here probability of B2B marketers ?=1780/5086=0.34998~ 0.350
hence from binomial distribution:
probability that from 10 marketers 7 B2B marketers are included =P(X=7)
= =0.0212
f)
for normal distribution z score =(p̂-p)/σ_{p} | |
here population proportion= p= | 0.350 |
sample size =n= | 200 |
std error of proportion=σ_{p}=√(p*(1-p)/n)= | 0.0337 |
hence based on the central limit theorem ; probability that the proportion of B2B marketers is between 50 to 70%:
probability = | P(0.5<X<0.7) | = | P(4.45<Z<10.38)~ | 1.0000-1.0000= | 0.0000 |
( please revert for any clarification required)
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