company manufacturing computer chips finds that 5% 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 company's 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.
A company manufacturing computer chips finds that 5% 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 company's 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 5%.
- Management thinks the incentive program did not work, when in fact it did lower the defective rate from 5%.
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 5%.
- Management thinks the incentive program did not work, when in fact it did lower the defective rate from 5%.
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 (4%, 6%). What conclusion should management reach about the new incentive program? Explain.
- Since 5% is not in the interval, we have enough evidence that the defect rate has been decreased.
- Since 5% is in the interval, we do not have evidence that the defect rate has been decreased.
e. Describe to management an advantage of decreasing the significance level.
- Lowers the
probability of a Type I error - Lowers the probability of a Type II error
f. Describe to management a disadvantage of decreasing the significance level.
- Raises the probability of a Type I error
- Raises the probability of a Type II error
g. Management decided to extend the incentive program so that the decision can be made on three months of data instead. Will the power increase, decrease, or remain the same with a larger sample size, assuming they use the same level of significance?
The power will
- Increase
- Decrease
- Stay the same
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