Question

It has been found that the average time Internet users spend online per week is 18.3 hours. A random sample of LaTeX: n=48 n = 48 teenagers indicated that their mean amount of Internet time per week is LaTeX: \bar{x}=20.9 x ¯ = 20.9 , with a population standard deviation of LaTeX: \sigma=5.7 σ = 5.7 hours. At the LaTeX: \alpha=0.02 α = 0.02 level of significance, can it be concluded that the mean time differs from 18.3 hours per week?

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 18.3

H_a : 18.3

Test statistic = z

= ( - ) / / n

= (20.9 - 18.3) / 5.7 / 48

Test statistic = 3.16

P(z > 3.16) = 1 - P(z < 3.16) = 0.0008

P-value = 2 * 0.0008 = 0.0016

= 0.02

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the  mean time differs from 18.3 hours per week .