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 Click here for the Excel Data File (a) Choose the appropriate hypotheses. Define the difference as Entry − Exit. H0: μd = 0 versus H1: μd ≠ 0 H0: μd ≥ 0 versus H1: μd < 0 H0: μd ≤ 0 versus H1: μd > 0 (b) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) tcalc (c) Find the critical value tcrit for α = 0.05. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) tcrit
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 |
Click here for the Excel Data File
(a) Choose the appropriate hypotheses. Define the difference as Entry − Exit.
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H0: μd = 0 versus H1: μd ≠ 0
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H0: μd ≥ 0 versus H1: μd < 0
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H0: μd ≤ 0 versus H1: μd > 0
(b) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)
tcalc
(c) Find the critical value tcrit for α = 0.05. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)
tcrit
(d) Find the p-value. (Round your answer to 4 decimal places.)
p-value
(e) State your conclusion.
We (Click to select) fail to reject reject the null hypothesis.
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