Presentation on theme: "Unlocking the Mysteries of Hypothesis Testing"— Presentation transcript:
1Unlocking the Mysteries of Hypothesis Testing Brent GriffinRevised Fall 2006
2What’s this all about? Hypothesis An educated guessA claim or statement about a property of a populationThe goal in Hypothesis Testing is to analyze a sample in an attempt to distinguish between population characteristics that are likely to occur and population characteristics that are unlikely to occur.
3The Basics Null Hypothesis vs. Alternative Hypothesis Type I vs. Type II Error vs.
4Null Hypothesis vs. Alternative Hypothesis Statement about the value of a population parameterRepresented by H0Always stated as an EqualityAlternative HypothesisStatement about the value of a population parameter that must be true if the null hypothesis is falseRepresented by H1Stated in on of three forms><
6Alpha vs. Beta a is the probability of Type I error b is the probability of Type II errorThe experimenters (you and I) have the freedom to set the -level for a particular hypothesis test. That level is called the level of significance for the test. Changing a can (and often does) affect the results of the test—whether you reject or fail to reject H0.
7Alpha vs. Beta, Part IIIt would be wonderful if we could force both and to equal zero. Unfortunately, these quantities have an inverse relationship. As increases, decreases and vice versa.The only way to decrease both and is to increase the sample size. To make both quantities equal zero, the sample size would have to be infinite—you would have to sample the entire population.
8Type I and Type II Errors True State of NatureThe nullhypothesis istrueThe nullhypothesis isfalseType I error(rejecting a truenull hypothesis)We decide toreject thenull hypothesisCorrectdecisionDecisionType II error(rejecting a falsenull hypothesis)page 376 of textWe fail toreject thenull hypothesisCorrectdecision
9Forming ConclusionsEvery hypothesis test ends with the experimenters (you and I) eitherRejecting the Null Hypothesis, orFailing to Reject the Null HypothesisAs strange as it may seem, you never accept the Null Hypothesis. The best you can ever say about the Null Hypothesis is that you don’t have enough evidence, based on a sample, to reject it!
10Seven Steps to Hypothesis Testing Happiness (Traditional or Classical Method)
11The Seven Steps…Describe in words the population characteristic about which hypotheses are to be testedState the null hypothesis, HoState the alternative hypothesis, H1 or HaDisplay the test statistic to be used
12The Seven Steps… Identify the rejection region Is it an upper, lower, or two-tailed test?Determine the critical value associated with , the level of significance of the testCompute all the quantities in the test statistic, and compute the test statistic itself
13The Seven Steps…State the conclusion. That is, decide whether to reject the null hypothesis, Ho, or fail to reject the null hypothesis. The conclusion depends on the level of significance of the test. Also, remember to state your result in the context of the specific problem.
14Types of Hypothesis Tests Large Sample Tests, Population Mean (known population standard deviation)Large Sample Tests, Population Proportion (unknown population standard deviation)Small Sample Tests, Mean of a Normal Population
15Actually, it’s just the beginning... The EndActually, it’s just the beginning...