Question

In 2006, the General Social Survey asked respondents how many hours they spent per week on the internet. The sample mean was 5.74 and the standard error of this estimate is 0.20. Construct a 95% confidence interval for the population mean number of hours spent per week on the internet.

Answer 1

(
`6.13, 5.348`)

Explanation:

Given -

Mean of the sample (μ)
`= 5.74`

Standard error (SE)
`= 0.20\\`

Significance level is equal to

`1 -0.95`

`= 0.05\\`

Critical value for this significance level

`z_(a/2) = 1.96`

Now the confidence interval for the population mean number of hours spent per week on the internet is given by

μ
`+ z_(a)/(2) * SE`

`= 5.74 + (1.96*0.20)\\= 6.13`

μ
`-z_(a)/(2) * SE`

`= 5.74 - (1.96*0.20)\\= 5.348`