Facebook has become a very popular website among senior citizens. A random sample of 65 senior...

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)

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Expert Solution

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} = t_0.005,64 = 2.655

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.655 * (25 / $\sqrt$ 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 )

orchestra answered 1 year ago

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