Question

1. A construction company that installs drywall wanted to investigate how a person’s age affects how much dry wall they can install in a week. On one hand, it would seem that the younger workers would be able to install more, but it seems that experience would also play a role. Two samples were taken.
   
   Ages 18-21 Ages 25-28
   (sheets / wk) (sheets / wk)
   88 104
   104 116
   96 96
   88 104
   112 108
   108 108
   84 116
   120 112
   92 120
   116 108
   
   a) Set up the null and alternative hypotheses to see if there is a difference in the average number of sheets of dry wall that a person can install per week based on age.
   b) Check the conditions.
   c) Calculate the test statistic.
   d) Find the p-value.
   e) Using α = 0.05, state your conclusion in the context of the problem.

Answer 1

a)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
      

b)

Normal approximation holds if the two sampled populations are similar and not too assymmetric          

c) Sample #1   ---->   1                  
mean of sample 1,    x̅1=   100.800                  
standard deviation of sample 1,   s1 =    12.900                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   109.200                  
standard deviation of sample 2,   s2 =    7.068                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    100.8000   -   109.2   =   -8.400  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    10.4009                  
std error , SE =    Sp*√(1/n1+1/n2) =    4.6514                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -8.4000   -   0   ) /    4.65   =   -1.806

d)

Degree of freedom, DF=   n1+n2-2 =    18
p-value =        0.0877

e)

p-value>α , Do not reject null hypothesis
there is no evidence that  there is a difference in the average number of sheets of dry wall that a person can install per week based on age.