a company manufacturing computer chips finds that 6% of all chips manufactured are defective. management is concerned that employee inattention is partially responsible for the high defect rate. in an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. the incentive program is instituted for one month. if successful, the company will continue with the incentive program.

a. write the companys null and alternative hypotheses. make sure to include the correct parameter, sign and number.

ho:

h1:

b. in this context describe a type i error and the impact such an error would have on the company.

management thinks the incentive program was effective, when in fact it did not lower the defective rate from 6%.

management thinks the incentive program did not work, when in fact it did lower the defective rate from 6%.

c. in this context describe a type ii error and the impact such an error would have on the company.

management thinks the incentive program was effective, when in fact it did not lower the defective rate from 6%.

management thinks the incentive program did not work, when in fact it did lower the defective rate from 6%.

d. based on the data they collected during the trial program, management found that a 95% confidence interval for the percentage of defective chips was (5%, 7%). what conclusion should management reach about the new incentive program? explain.

Question

a company manufacturing computer chips finds that 6% of all chips manufactured are defective. management is concerned that employee inattention is partially responsible for the high defect rate. in an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. the incentive program is instituted for one month. if successful, the company will continue with the incentive program.

a. write the companys null and alternative hypotheses. make sure to include the correct parameter, sign and number.

ho:

h1:

b. in this context describe a type i error and the impact such an error would have on the company.

management thinks the incentive program was effective, when in fact it did not lower the defective rate from 6%.

management thinks the incentive program did not work, when in fact it did lower the defective rate from 6%.

c. in this context describe a type ii error and the impact such an error would have on the company.

management thinks the incentive program was effective, when in fact it did not lower the defective rate from 6%.

management thinks the incentive program did not work, when in fact it did lower the defective rate from 6%.

d. based on the data they collected during the trial program, management found that a 95% confidence interval for the percentage of defective chips was (5%, 7%). what conclusion should management reach about the new incentive program? explain.

Accepted Answer

# a.
## Brief Explanations:
The null hypothesis ($H_0$) is a statement of no change. Here, the parameter is the proportion $p$ of defective chips. The company wants to test if the defect rate has decreased. So, $H_0:p = 0.06$ (the defect rate is still $6\%$). The alternative hypothesis ($H_1$) is the claim we are trying to find evidence for. Since we want to see if the defect rate has decreased, $H_1:p<0.06$.

# Answer:
$H_0:p = 0.06$
$H_1:p<0.06$

# b.
## Brief Explanations:
A Type - I error is rejecting the null hypothesis ($H_0$) when it is true. In this context, $H_0$ is that the defect rate $p = 0.06$. So, a Type - I error is when management thinks the incentive program was effective (rejects $H_0$: concludes $p < 0.06$), but in reality, the defect rate did not lower from $6\%$ ( $H_0$ is true). The impact is that the company may continue an ineffective incentive program, wasting resources.

# Answer:
Management thinks the incentive program was effective, when in fact it did not lower the defective rate from $6\%$.

# c.
## Brief Explanations:
A Type - II error is failing to reject the null hypothesis ($H_0$) when it is false. Here, $H_0:p = 0.06$ and $H_1:p<0.06$. So, a Type - II error is when management thinks the incentive program did not work (fails to reject $H_0$: does not conclude $p < 0.06$), but in reality, the defect rate did lower from $6\%$ ( $H_0$ is false). The impact is that the company may discontinue an effective incentive program, missing an opportunity to reduce costs (from fewer defective chips).

# Answer:
Management thinks the incentive program did not work, when in fact it did lower the defective rate from $6\%$.

# d.
## Brief Explanations:
A $95\%$ confidence interval for the proportion of defective chips is $(0.05,0.07)$. The null hypothesis value $p = 0.06$ is within this confidence interval. When the hypothesized value (from $H_0$) is within the confidence interval, we fail to reject the null hypothesis.

# Answer:
Management should not reject the null hypothesis. Since the $95\%$ confidence interval $(5\%,7\%)$ contains the hypothesized value of $6\%$, there is not enough evidence to conclude that the incentive program has changed (lowered) the defect rate. So, the company may not continue the incentive program based on this data.

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QUESTION IMAGE

Question

Explanation:

a.

Answer:

b.