Question 1183829
a. The sample was collected to determine whether the belief that the average number of Facebook friends of 338 is still true.


b. The signicance level is {{{alpha = 0.05}}}, no need to calculate.  (But do you know what this value means?)


c.  By the CLT, the sampling distribution of the sample means is approximately normally distributed with mean {{{mu = 338}}}, and standard dev {{{sigma/sqrt(n) = 43.2/sqrt(50)}}}.

===> critical value for a ONE-TAILED test (will explain later why)  is 1.645.


d.  {{{z = ((X-bar) - mu)/(sigma/sqrt(n)) =  (350 - 338)/(43.2/sqrt(50)) = 1.964}}}


e.  By comparing the test value with the critical z, we reject the null hypothesis, and conclude that 
there is evidence that the average number of Facebook friends may have increased from 338.


f.  It is a one-tailed test because the sample value of 350 is quite far from 338 (on the high side), enough to suspect that the 
true sample mean may have increased from 338.


g.  Maximum error is given by {{{z[0.95]*(sigma/sqrt(n)) = 1.645*(43.2/sqrt(50)) =  10.05}}}


Done.