Question

Robin Dunbar, a leading anthropologist at Oxford University who studies social networks, has suggested that there is a magical number for social networks that humans can manage: any grouping larger than 150 people becomes overwhelming. With that in mind, a group of researchers at facebook wanted to study more about how their average user manages their social networks. In particular they wanted to study the users with the highest friend counts to see how they managed. They took a random sample from users who were in the top 15% when their users were arranged according to their friend count. This study of these 225 facebook users found a mean of 520 friends. Facebook knows from prior studies of their users that the standard deviation is 46. Question 2 of 7 Based on this information, what would be the point estimate for μ? 225, 520, 46, 150, None of the above

Question 3 of 7 We are 95% confident that the mean number of friends that facebook users have is: between 516.93 and 523.07 between 428 and 612 between 513.87 and 526.13 between 474 and 566 between 510.79 and 529.21 Question 4 of 7 This is not quite right. It seems that you have found a 99.7% confidence interval for the mean rather than a 95% confidence interval for the mean. Consider the remaining options. :

Using a sample of size 400 (instead of 225).

Using a sample of size 36 (instead of 225). Using a different sample of size 225.

Using a 90% level of confidence (instead of 95%). Using a 99% level of confidence (instead of 95%).

Both using a sample of size 400 (instead of 81) and using a 90% level of confidence (instead of 95%) are correct.

Both using a sample of size 400 (instead of 225) and using a 90% level of confidence (instead of 95%) are correct.

Question 5 of 7 How large a sample of facebook users is needed in order to estimate μ with a 95% confidence interval of length 14.16 friends? 900, 144, 625, 841, 169

Answer 1

SOLUTION 2: AS WE KNOW SAMPLE MEAN IS AN UNBIASED ESTIMATE OF POPULATION.SO the point estimate for μ is 520.

SOLUTION 3:

M = 520
Z = 1.96
s_M = √(46²/225) = 3.07
μ = M ± Z(s_M)
μ = 520 ± 1.96*3.07
μ = 520 ± 6.017

95% CI [513.983, 526.017].

You can be 95% confident that the population mean (μ) falls between 513.983 and 526.017

between 513.87 and 526.13

SOLUTION 4:Both using a sample of size 400 (instead of 225) and using a 90% level of confidence (instead of 95%)

SOLUTION 5:

14.16= 2*46*1.96/sqrt(n)

7.08= 46*1.96/sqrt(n)

sqrt(n)= 12.73= 13

n= 169