Question

You have a production line that has historically resulted in scores normally distributed about a mean of: 1,366.00 and a standard deviation of 692.00 . You felt that you could do better and improve operations. You conducted the below tests resulting with the provide normally distributed sample responses. Your manager claims it yields the same mean results as the historical system but you are unsure. While it is a more efficient processyou are unwilling to update the process if the new system is not calibrated to the same mean as the old system. Determine the p-value associated with this hypothesis test assuming that σ=692.00 Conduct the stepped approach similar to as discussed in class. Furthermore, clearly state your conclusions about the hypothesis. An appropriate number of decimal points should be taken which will differbased on step of solution. Your p-value should include 6 decimal places. Stop solving the question once you reach the p-value in the due process.

Answer 1

To perform the hypothesis test, use the z-distribution and calculate the p-value to determine the probability of obtaining a sample mean as extreme or more extreme than the observed value, assuming the null hypothesis is true.

Step-by-step explanation:

To perform the hypothesis test in this scenario, you would use the z-distribution. Since the underlying population is assumed to be normal and the sample size is large enough, the z-distribution is appropriate. To calculate the p-value, you would compare the sample mean (12.8) to the population mean (13) using the formula z = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Once you have the z-score, you can find the corresponding p-value using a standard normal distribution table or a calculator. The p-value indicates the probability of obtaining a sample mean as extreme or more extreme than the observed value, assuming the null hypothesis is true.