A company that produces valves wants to error test the valves. 12% of all produced valves gave at least (at least) one error. It is done some changes to the production process to try to reduce the amount of produces valves with errors. After the changes in the production process is done, the company wants to find out if the changes has had some effects. This will be done by preforming a hypothesis test with a 5% significant value based on the information they get from counting the number of valves with errors they find in a production with n independent valves. a) Formulate the issue as a hypothesis test. b) If the amount of valves with errors after the changes is 10%, what is the probability for the test to discard(what is the strength of the test) ifn = 100? c) Calculate the strength of the test if n = 100 and the amount of errors after the changes is 8%. d) If you would want a probability at 90% for the test to discard (strength at 90%) if the amount of errors after the changes is about 8%, how many valves, n, have to be tested?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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