Question

6) The average amount of sleep a teen gets on Sundays is 7.8 hours. A researcner reeis unat ume average time is greater than 7.8 hours. The researcher collects data from 24 teens in a particular k and finds that the mean number of hours a teen sleeps on Sunday is 7.9 hours with a standard tion of.27 hours. At a .05, is there enough evidence to say that teens sleep more than 7.8 hours on Sundays? Solve the problem by showing each of the five steps we used in class. Show work with formula. Use the 1. 2. 3. 4. 5 4 3 2 1

Answer 1

step 1)

Ho :   µ =   7.8      
Ha :   µ >   7.8       (Right tail test)

step2 )

Level of Significance ,    α =    0.05
critical t value, t* =        1.714   [Excel formula =t.inv(α/no. of tails,df) ]
reject Ho, if test  stat > 1.714

step 3)

sample std dev ,    s =    0.270                  
Sample Size ,   n =    24                  
Sample Mean,    x̅ =   7.900                  
                          
degree of freedom=   DF=n-1=   23                  
                          
Standard Error , SE = s/√n =   0.270   / √    24   =   0.055      
t-test statistic= (x̅ - µ )/SE = (   7.90   -   7.8   ) /    0.055   =   1.814

step 4)

Decision; since, test stat = 1.814> 1.714 , reject HO

step 5)

Conclusion: There is enough evidence to conclude that teens sleep more than 7.8 hours on sundays at α=0.05