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	41	52	58	61	53	49	45
Exit failures	45	52	59	60	57	45	51	47

(b) Find the test statistic t_calc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

t_calc         

(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.)

t_crit        

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

p-value          

Answer 1

x	y	d	d-mean	(d-mean)^2
44	45	-1	0.625	0.390625
41	52	-11	-9.375	87.89063
52	59	-7	-5.375	28.89063
58	60	-2	-0.375	0.140625
61	57	4	5.625	31.64063
53	45	8	9.625	92.64063
49	51	-2	-0.375	0.140625
45	47	-2	-0.375	0.140625

Mean	-1.625
s=Sqrt(∑(d-mean)^2/(n-1))	5.878
standard Error=s/sqrt(n)	2.078268
Test Staistic= d mean/(s/sqrt(n))	-0.782
alpha	0.05
Critical Value	2.365

(b) Find the test statistic t_calc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

t_calc = -0.782  

(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.)

t_crit = 2.365,- 2.365

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

p-value = 0.4599