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# Hypothesis testing

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### Hypothesis testing

1. 1. Hypothesis testing
2. 2. • Hypothesis-*A tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation.*Something taken to be true for the purpose of argument or investigation; an assumption.*An educated guess based on observation.Eg: Avogadro’s hypothesisTheory- Explain a large class of observations through a model and have predictive capability which can be testedEg: Einstein’s theory of relativityLaw- Generalizes a body of observations -A statement of fact meant to describe, in concise terms, an action or set of actions. It is generally accepted to be true and universalEg: Newton’s Law of gravitation
3. 3. • Null hypothesis: the assumption we wish to test Ho• Alternate hypothesis : when we reject the null hypothesis• Type 1 error: Rejecting a null hypothesis when it is in fact true• Type 2 error: Accepting a null hypothesis when it is false
4. 4. • The roofing contract for a sports complex requires the roofing sheets to be 0.04 inches thick. The sports complex samples a lot of 100 sheets from a supply of 10,000 sheets and finds the sample mean is 0.0408 inches. From past experience it is known that these sheets come from a thickness population with standard deviation of 0.004 inches. On the basis of the sample data the sports complex must decide whether or not to accept the consignment of 10,000 sheets
5. 5. • The basic question is, “if the true mean is 0.04 what are the chances of getting a sample with a mean thickness of 0.0408?”If the probability of getting such a sample is very low, then we must conclude that the true mean is not really 0.04
6. 6. • Calculate standard error of the mean• Calculate z=2• So probability of the sample mean being less than 0.0392 or larger than 0.0408 is 4.5%
7. 7. • A manufacturer supplies axles for trucks. These axles must be able to withstand a 80000 psi in stress tests, but an excessively strong axle will increase production costs. A sample of 100 axles from production has a mean strength of 79600 psi. Experience indicates that the standard deviation of the strength of the axles is 4000 psi.If the axle manufacturer uses a significance of 0.05, should he accept the axles?
8. 8. • Ho- The axles are from a population with a mean of 80,000• H1- The true mean is not 80,000