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=.01\alpha=.01.

 Truck 1  Truck 2  Truck 3  Truck 4  Truck 5  Truck 6  Truck 7  Truck 8  Entry failures 4345535661514844 Exit failures 4851605858455550\begin{array}{lcccccccc} \hline & \text { Truck 1 } & \text { Truck 2 } & \text { Truck 3 } & \text { Truck 4 } & \text { Truck 5 } & \text { Truck 6 } & \text { Truck 7 } & \text { Truck 8 } \\ \hline \text { Entry failures } & 43 & 45 & 53 & 56 & 61 & 51 & 48 & 44 \\ \text { Exit failures } & 48 & 51 & 60 & 58 & 58 & 45 & 55 & 50 \\ \hline \end{array}

Solution

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Answered 1 year ago
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For the two given data samples, we can calculate that their differences (d)(d) are: 'slader'

Using the functions for mean and standard deviation: AVERAGE(Difference) and STDEV.S(Difference)

we can find out that the mean value of all differences is dˉ=3.00\bar{d}=-3.00 and its standard deviation sd=4.957s_d=4.957. Also, as we can count from the table, the sample size is n=8n=8.

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