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 490 cables. The cables were examined and there were 11 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

If we compare the p value and the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives for robots is not significantly lower than the proportion of defectives for human

Step-by-step explanation:

Data given and notation

n=490 represent the random sample taken

X=11 represent the number of defectives for robots

estimated proportion of defectives for robots

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of defectives for robots is lower than for the humans :  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed for this case is . The next step would be calculate the p value for this test.  

Since is a lower tail test test the p value would be:  

If we compare the p value and the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives for robots is not significantly lower than the proportion of defectives for human

answer: a clock

step-by-step explanation:

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step-by-step explanation:

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