In: Statistics and Probability
Facebook has become a very popular website among senior citizens. A random sample of 65 senior Americans showed a sample average of 189 friends with a sample standard deviation of 25 friends. Estimate the number of Facebook friends senior Americans have in a 99% confidence interval.
(Do not use direct steps)
Solution :
Given that,
= 189
s = 25
n = 65
Degrees of freedom = df = n - 1 = 65 - 1 = 64
At 99% confidence level the t is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
t /2 df = t0.005,64 = 2.655
Margin of error = E = t/2,df * (s /n)
= 2.655 * (25 / 65)
= 8.2
The 99% confidence interval estimate of the population mean is,
- E < < + E
189 - 8. 2< < 189 + 8.2
180.8 < < 197.2
( 180.8, 197.2 )