Question

A sample of 337 subscribers to Wired magazine shows the mean time spent using the Internet is 14.4 hours per week, with a sample standard deviation of 5.8 hours.

Find the 80% confidence interval for the mean time Wired subscribers spend on the Internet. (Round the final answers to 2 decimal places.)

The confidence interval is between  and  .

Answer 1

Solution :

Given that,

= 14.4

s =5.8

n =337

Degrees of freedom = df = n - 1 = 337- 1 = 336

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10,336 =1.284 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.284 * (5.8 / 337)

= 0.41

The 80% confidence interval is,

- E < < + E

14.4 -0.41 < <14.4 + 0.41

13.99 < < 14.81

( 13.99 , 14.81)