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	40	45	53	55	64	54	49	44
Exit failures	50	53	58	60	59	46	54	45

(a) Choose the appropriate hypotheses. Define the difference as Entry − Exit.

• H₀: μ_d = 0 versus H₁: μ_d ≠ 0

• H₀: μ_d ≥ 0 versus H₁: μ_d < 0

• H₀: μ_d ≤ 0 versus H₁: μ_d > 0

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

t_calc?   

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

What is the p-value?

Answer 1

Test Statistics,

t cal -0.840

Critical Value,

tcri = 2.571

P value = 0.4390

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