Question

36. Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. (Let d = Machine A - Machine B.)Productivity Rate

Person	Machine A	Machine B
1	47	52
2	53	58
3	50	47
4	55	60
5	45	53

please explain and show all work --- do NOT use excel commands/excel to solve this problem

a.         State the null and alternative hypotheses for a two-tailed test.

            b.   Find the mean and standard deviation for the difference.

            c.   Compute the test statistic.

            d.   Test the null hypothesis stated in Part a at the 10% level.

Answer 1

a)

Ho :   µd=   0
Ha :   µd ╪   0

b)

paired t test

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
47	52	-5	1
53	58	-5	1
50	47	3	49
55	60	-5	1
45	53	-8	16
	total	-20	68

mean of difference ,    D̅ =ΣDi / n = -20/5 = -4
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) = √(68/4) =   4.1231

c)

std error , SE = Sd / √n =    4.1231   / √   5   =   1.8439      
                          
t-statistic = (D̅ - µd)/SE = (   -4   -   0   ) /    1.8439   =   -2.169

d)

α=0.10

Degree of freedom, DF=   n - 1 =    4
t-critical value , t* =    ±   2.132 [from t table ]

since, test stat = -2.169 < -2.132, Reject null hypothesis

conclusion: there is enough evidence to conclude that there is difference in productivity rate on both machines at significance level of 10%