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6 November, 18:14

Scientists think that robots will play a crucial role in factories in the next several decades. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 507 cables. The cables were examined and there were 9 defectives. If human assemblers have a defect rate of 0.035 (3.5%), does this data support the hypothesis that the proportion of defectives is lower for robots than humans

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  1. 6 November, 18:25
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    The data support the hypothesis that the proportion of defectives is lower for robots than humans.

    Step-by-step explanation:

    To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.

    From the data given:

    Total number of cables a robot assembled = 507

    Defectives = 9

    To get the defect rate = the number of defects divided by the total number of cables, multiplied by 100.

    Defect rate = (9 / 507) x 100 = 0.01775 x 100

    Defect rate for the robot = 1.775‬%

    From the question, a robot was used and the defect rate after the calculation is 1.775‬%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745‬ defectives.

    x / 507 = 3.5%

    x (defectives) = 17.745‬

    Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.
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