1. How will marketers change their social media use in the...

1. 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 (a) Define two variables used in the survey data. Define the sample space of each variable. (b) Suppose a marketer is selected at random, what is the probability that he or she is a B2B marketer? (c) Given that a B2B marketer is selected, what is the probability that the marketer plans to increase use of LinkedIn? (d) Are the two variables in (a) are independent? Explain based on probability values. (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 sample? (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)

Transcript

00:01 Now in this question, you have a survey, right, which reported that 76 % of the b2b marketers are planning to increase the use of ninkth in, right, as compared to 22 % of b2c marketers.

00:13 The survey was based on this many marketers and these many b2c marketers.

00:19 And the data are giving this question, right? so defined two variables using the survey data.

00:23 Well, there are two variables.

00:24 One is, of course, the type of, you know, the type of business focus, right? it could be two b2b or b2c, right? so this is the first one, the business focus.

00:35 There's one valuable.

00:36 And the second one is the linkedin, right? the proportion of nkdn, right? a use of nkdn, right? so that's the two variables, right? for the business focus, of course, we only two values, right, b2b or p2c.

00:50 For the increased use of nicb or not, again, it has only two possibilities, yes or no.

00:57 So those are some of the spaces for.

00:59 Is validables.

01:00 And as opposed to market, it's a circular random, what's probably that he's a b2b marker? well, b2b, obviously, together, all together, you have, you know, this, this menu, right? 1, 17 for this and a b2c for this, right? the total is this, right? so the probability, of course, is given by 1 ,780 divided by 5086, right? so, and you can do the calculation, and you find that to be actually given by 1 ,7 .80 divided by 5086.

01:35 And that gives you actually 35%.

01:38 And how about if you have a b2b marketer, what is probably that market plans increase you? so you look at a b2b marketer, right? and what the plan are going to increase? well, that's this number, right? so the probability is given by 1 ,353 divided by 1 .7.

01:58 So that's given by 1 353 divided by 1780.

02:06 So i found this to be actually 76%.

02:11 Are the two variables independent or not? so basically you are asking whether these two variables are independent or not.

02:20 And clearly they're not independent.

02:23 The reason you can see is that if you look at the probability values, the developers of use are not independent, right? the two variables, i mean, the use of eni and the business focus, right? the probability will depend on whether, you can see that the probability of use depend on whether you are looking at b2b or b2c, right? and so you can see that they're not independent, right? so the answer is known.

02:57 The reason is because the probability depends on whether you have b2b or b2c, right? i mean, in other words, the distribution of the b2b marketers against the increased use of lincoln inn is different from the distribution of the b2c marketers against the use of lincoln inn, right? as a result, they're not independent, right? so no, the answer is no.

03:26 If 10 marketers out of 5 ,000 and 86 survey respondents were circled random as a sample, what's probably that seven marketers are included in the sample? well, that, of course, it's given by, you know, this is a binomial distribution, right? so seven out of 10, right? as you can see that, as you can see that the probability, the probability for one market to be b2b tab is given by, as we said, 35%.

04:00 So the probability for this case, of course, is given by 7 .35 % to 0 .35, onto the power of 7 multiplied by 0 .65, which is the complement, part to 10 minus 7, 10 ,000, that 3, right? and they multiply the possibility you have 7 out of 10, right? so it's given by 10 factor divided 1.

04:21 Three factor divided by the same factor.

04:24 And if you do the calculation, you find this to be given by.

04:29 I found this actually gave you by about 2 .1%.

04:33 So that's my probability.

04:37 If 200 marketers out of this survey response will select random as a sample, what's probably the proportion of this in the sample is between 100 and 140...

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