What probability value should be used for determining whether the modified process results in a defect rate that is less than 6%.
I got part a and b of the question but I am completely lost on what this is asking me. Can anyone help?!?
Of course! I can help you understand the question.
The question is asking for the probability value that should be used to determine whether a modified process results in a defect rate that is less than 6%. In other words, the probability value will help determine whether the modified process is effective in reducing the defect rate to below 6%.
To find the probability value, you will need to use statistical methods such as hypothesis testing. Here's a step-by-step approach to help you:
1. Formulate the null and alternative hypotheses:
Null hypothesis (H0): The defect rate of the modified process is equal to or greater than 6%.
Alternative hypothesis (Ha): The defect rate of the modified process is less than 6%.
2. Choose a significance level (α): This is the threshold value at which you would reject the null hypothesis. Commonly used significance levels are 0.05 or 0.01.
3. Collect data: Gather data on the defect rates from the modified process. This data will be used to calculate the test statistic.
4. Calculate the test statistic: Depending on the type of data (e.g., discrete or continuous), you will use a specific statistical test such as the binomial test or the t-test.
5. Determine the p-value: The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. You can use statistical software or tables to obtain the p-value.
6. Compare the p-value to the significance level: If the p-value is less than the chosen significance level, you would reject the null hypothesis. If the p-value is greater than the significance level, you would fail to reject the null hypothesis.
7. Interpret the results: If you reject the null hypothesis, it suggests that the modified process does result in a defect rate that is less than 6%. If you fail to reject the null hypothesis, it suggests that there is not enough evidence to conclude that the modified process has effectively reduced the defect rate.
By following these steps, you can determine the probability value (p-value) that will help you make a decision about the defect rate of the modified process.