Scientists think that robots will play a crucial role in factories in the next s

Question

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 505 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? Use a 0.01 significance level.
State the appropriate null and alternative hypotheses.

State the rejection region(s). If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.

Compute the test statistic value. Round your answer to two decimal places.
z =  

State the conclusion in the problem context.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the defect rate is lower for robots.Do not reject the null hypothesis. There is sufficient evidence to conclude that the defect rate is lower for robots.    Reject the null hypothesis. There is not sufficient evidence to conclude that the defect rate is lower for robots.Reject the null hypothesis. There is sufficient evidence to conclude that the defect rate is lower for robots

Explanation / Answer

Answer to the question)

Null hypothesis: ho: p = 0.035

Alternate hypothesis: ha: p < 0.035

it is a left tailed test

significance level 0.01

thus the z critical value will be = -2.33

Rejection region = z < -2.33

.

Sample data

sample size n = 505

number of defectives x = 11

sample proprotion p^ = 11/505 = 0.0218

.

SE = sqrt(p*q/n)

SE = sqrt(0.035*0.965 /505)

SE = 0.00818

.

formula of test statistic is:

z = (p^-P) / SE

z = (0.0218 -0.035) / 0.00818

z = -1.61

.

Ineference: Since Z statistic -1.61 > z critical -2.33, we fail to reject the null hypothesis

Conclusion: As we fail to reject the null hypothesis this implies the true population proportion is 0.035

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