Question

A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a significant difference between entry and exit gate failures? Use α = 0.05.

	Truck 1	Truck 2	Truck 3	Truck 4	Truck 5	Truck 6	Truck 7	Truck 8
Entry failures	44	40	55	56	62	52	45	45
Exit failures	50	53	55	56	55	50	51	47

(c) Find the critical value t_crit for α = 0.05. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)



(d) Find the p-value. (Round your answer to 4 decimal places.)

  

Answer 1

Assumptions: Let us assume that the data follows a Normal distribution with same variance and are independent.

The given data is:

	Entry	Exit
Truck 1	44	50
Truck 2	40	53
Truck 3	55	55
Truck 4	56	56
Truck 5	62	55
Truck 6	52	50
Truck 7	45	51
Truck 8	45	47

Null Hypothesis: There is no difference between entry and exit gate failures.

Alternative Hypothesis: There is a significant difference between entry and exit gate failures

Level of significance

Test statistic:

follows a t with 14 df. and

We have   

     

The critical value of t is 2.145. Since the calculated value is less than the critical value, we do not reject the null hypothesis. Hence there is no significant difference between entry and exit gate failures.

b).The p-value is found by the EXCEL function T.DIST.2T(0.782,14) and is 0.4472.