Question

Conduct a hypothesis test. Perform each of the following steps:

a) state the hypothesis and identify the claim

b) Find the critical value(s)

c) Compute the test value

d) make the decision

e) Summarize the results

It has been found that the average time users spend online per week is 18.3 hours. A random sample of 48 teenagers indicated that their mean amount of Internet time per week was 19.5 hours with a population standard deviation of 5.7. At the 0.05 level of significance, can it be concluded that the mean time differs from 18.3 hours per week?

Answer 1

Solution :

= 18.3

= 19.5

= 5.7

n = 48

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 18.3

Ha : 18.3

Test statistic = z

= ( - ) / / n

= (19.5 -18.3) / 5.7 / 48

= 1.459

p(Z >1.459 ) = 1-P (Z < 1.459 ) = 0.1512

P-value = 0.1512

= 0.05  

0.1512 >0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that  

It be not concluded that the mean time differs from 18.3 hours per week.