Question

Suppose that a delivery truck, while on its route on six randomly selected days, made an average of 14 deliveries per day with a standard deviation of 2 deliveries. A second delivery truck, while on another route on seven randomly selected days, made an average of 12 deliveries per day with a standard deviation of 4 deliveries. Can we assert at the level of signifcance a=0.05 that the first delivery truck on its route makes a larger number of deliveries than the second delivery truck on its route?

Answer 1

Data:     

n1 = 6    

n2 = 7    

x1-bar = 14    

x2-bar = 12    

s1 = 2    

s2 = 4    

Hypotheses:    

Ho: μ1 ≤ μ2    

Ha: μ1 > μ2    

Decision Rule:    

α = 0.05    

Degrees of freedom = 6 + 7 - 2 = 11

Critical t- score = 1.79588481   

Reject Ho if t > 1.79588481   

Test Statistic:    

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((6 - 1) * 2^2 + (7 - 1) * 4^2)/(6 + 7 - 2)) = 3.247376564

SE = s * √{(1 /n1) + (1 /n2)} = 3.24737656354395 * √((1/6) + (1/7)) = 1.806673536

t = (x1-bar -x2-bar)/SE = (14 - 12)/1.80667353555347 = 1.107006861

p- value = 0.14595578    

Decision (in terms of the hypotheses):

Since 1.10700686 < 1.795884814 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the first delivery truck on its route makes a larger number of deliveries than the second delivery truck on its route.