You have been put in charge of the Quality Control systems for the resistor produc- tion line that your company has developed.
Run PF4NumberGen.m in MATLAB with your student number to generate your data for this portfolio. The code will output the data, and print out some key values and permissible assumed values. Do not use Octave.
The key process in the production line requires a resistor to be within a specific range of resistance. If the resistance lies outside this range, it is faulty and must be discarded.
1. You start the process to generate 50 units of the resistor. The resistances are measured, and the values recorded (see data from PF4NumberGen.m).
Write a single m file function that calculates and returns the sample mean (x¯) and sample variance (s2) of your data, using a for loop. Do not use built-in functions (you may use length or size, or hardcode the size of the array). Provide the code and the resulting mean and variance.
2. The process is supposed to have a mean value of µ (as per printout from PF4NumberGen.m). There are concerns that the system may be incorrectly calibrated. Determine the 95% confidence interval for the mean value, and perform a hypothesis test to determine if there is sufficient evidence to sup- port the concerns.
3. In order to be within tolerance, the resistance must be between µ - α and
µ + α (see printout from PF4NumberGen.m). If it is outside of this range, the resistor is defective. Assuming that the system produces resistances de- scribed by a Normal distribution with mean x¯ and variance s2, determine the probability that the resistor will be defective. You may use MATLAB or the Z-table.
4. Each packet contains 10 of these resistors, and the packet is acceptable as long as at least 8 of them are within tolerance. Determine the probability that the packet will be unacceptable.
5. The production line has been running for a while, and it has been observed that a glitch occurs approximately once every n days on average (see printout from PF4NumberGen.m), after which the system needs to be restarted. What is the probability that the system will need to be restarted more than 3 times in the next 31 days?
6. The boss has decided that the frequency of the glitches is unacceptable, and has ordered the critical component of the production line to be replaced with a newer, more expensive model. This newer model is supposed to improve stability so that the glitch only occurs approximately once every m days on average (find the value of m from PF4NumberGen.m). Upon installing, the glitch occurs within 24 hours. It is suspected that the manufacturer of the component has shipped the older model (that typically glitches every n days) by mistake. Calculate the probability that each model of the component will cause a glitch within the next 24 hours.
7. The manufacturer asserts that, at most, they mistakenly send the wrong model just 1% of the time. Assuming the manufacturer is telling the truth, use Bayes' Rule to determine the probability that it is the older model given that it failed within 24 hours.