An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let p denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02. (a) Which of the following pairs of hypotheses should the manufacturer testH_0: p=0.02 versus H_a: p<.02orH_0: p=0.02 versus H_a: p>.02Explain your answer.b. In the context of this exercise, describe Type I and Type II errors. c. Would you prefer a test with α= .01 or α= .1? Explain your reasoning.

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

To test whether the proportion of defective installations is less for the robots than for human assemblers use a single-proportion z-test.

(a)

The hypothesis can be defined as:

H₀: The proportion of defective installations is same for both the robots and human assemblers, i.e. p = 0.02.

Hₐ: The proportion of defective installations is less for the robots than for human assemblers, i.e. p < 0.02.

The alternate hypothesis is the claim or the statement that is being tested.

In this case we need to test whether the proportion of defective installations is less for the robots than for human assemblers or not, so that the manufacturer can decide whether they want to apply the conversion.

Thus, the correct option is:

H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b)

A type I error occurs when we discard a true null hypothesis and a type II error is made when we fail to discard a false null hypothesis.

In this case a type I error will be committed if conclude that the proportion of defective installations is less for the robots than for human assemblers when in fact it is not.

And a type II error will be committed if we fail to conclude that proportion of defective installations is less for the robots than for human assemblers.

(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (α).

Lesser the significance level of the test the lesser is the power of the test.

If the value of α is reduced from 0.05 to 0.01 then the region of acceptance will increase. This implies that there is low probability of rejecting the null hypothesis even when it is false.

So higher the value of α the higher is the probability of making a correct decision.

Thus, the better value of α will be 0.10.

tallinn tallinn · Answer 2 · 2021-12-27T17:05:12+01:00

correct option are:

(a) H₀: p = 0.02 vs. Hₐ: p < 0.02.

The value will be 0.10.

An automobile manufacturer is also considering using a robot for part of its assembly in the process only when if there is strong evidence that is the proportion of defective or installations is less the robots than the human assemblers.

But In a test, the proportion of defective or installations is less the robots than human assemblers use a single-proportion z-test is:

(a) when The hypothesis can be defined as H₀

the proportion of defective installations is the same But, for both the robots and also, in a human assembler, i.e. p = 0.02.

Now, Hₐ: The proportion of defective or installations is less than the robots human assemblers, i.e. p < 0.02.

Then, The alternate hypothesis is the claim or statement is being tested.

case: we need to test whether the proportion of defective or installations is less the robots than human assemblers or not, so that is why the manufacturer can decide whether they want to apply.

H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b) when a type I error occurs then we discard a true null hypothesis and a type II error is made so, we fail to discard a false null hypothesis.

When In this case, a type of I error will be committed if it concludes that the proportion of defective installations is less for the robots than for human assemblers it is not.

In a type of II error will be committed that if we fail to conclude then the proportion of defective installations is less for the robots than human assemblers.

(c) The power of the test is the probability of rejecting a null hypothesis or false

The power of the test is affected by the significance of the level of the test (α).

So, the Lesser the significance level of the test its the power of a test.

The value of α is reduced from 0.05 to 0.01 the region of acceptance will be increased. low probability of rejecting the null hypothesis or false.

So correct decision will be a higher the value of α the higher is making of the probability.

Thus, the good value of α will be 0.10.

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