• 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
• 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
• 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
• 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
• 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%
• 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?
• Ho- The axles are from a population with a mean of 80,000• H1- The true mean is not 80,000