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1、Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-1,Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests,Business Statistics: A First Course5th Edition,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-2,Learning Objectives,In this chapter, you learn: The basic pr
2、inciples of hypothesis testing How to use hypothesis testing to test a mean or proportion The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are seriously violated How to avoid the pitfalls involved in hypothesis testing The ethical issues involv
3、ed in hypothesis testing,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-3,What is a Hypothesis?,A hypothesis is a claim (assertion) about a population parameter: population mean population proportion,Example: The mean monthly cell phone bill in this city is = $42,Example: The proport
4、ion of adults in this city with cell phones is = 0.68,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-4,The Null Hypothesis, H0,States the claim or assertion to be tested Example: The average number of TV sets in U.S. Homes is equal to three ( ) Is always about a population parameter,
5、 not about a sample statistic,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-5,The Null Hypothesis, H0,Begin with the assumption that the null hypothesis is true Similar to the notion of innocent until proven guilty Refers to the status quo or historical value Always contains “=” , “
6、” or “” sign May or may not be rejected,(continued),Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-6,The Alternative Hypothesis, H1,Is the opposite of the null hypothesis e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: 3 ) Challenges the status quo Never con
7、tains the “=” , “” or “” sign May or may not be proven Is generally the hypothesis that the researcher is trying to prove,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-7,The Hypothesis Testing Process,Claim: The population mean age is 50. H0: = 50, H1: 50 Sample the population and f
8、ind sample mean.,Population,Sample,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-8,The Hypothesis Testing Process,Suppose the sample mean age was X = 20. This is significantly lower than the claimed mean population age of 50. If the null hypothesis were true, the probability of gett
9、ing such a different sample mean would be very small, so you reject the null hypothesis . In other words, getting a sample mean of 20 is so unlikely if the population mean was 50, you conclude that the population mean must not be 50.,(continued),Basic Business Statistics, 11e 2009 Prentice-Hall, Inc
10、.,Chap 9-9,The Hypothesis Testing Process,Sampling Distribution of X, = 50 If H0 is true,If it is unlikely that you would get a sample mean of this value .,. then you reject the null hypothesis that = 50.,20,. When in fact this were the population mean,X,(continued),Basic Business Statistics, 11e 20
11、09 Prentice-Hall, Inc.,Chap 9-10,The Test Statistic and Critical Values,If the sample mean is close to the assumed population mean, the null hypothesis is not rejected. If the sample mean is far from the assumed population mean, the null hypothesis is rejected. How far is “far enough” to reject H0?
12、The critical value of a test statistic creates a “line in the sand” for decision making - it answers the question of how far is far enough.,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-11,The Test Statistic and Critical Values,Critical Values “Too Far Away” From Mean of Sampling Di
13、stribution,Sampling Distribution of the test statistic,Region of Rejection,Region of Rejection,Region of Non-Rejection,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-12,Possible Errors in Hypothesis Test Decision Making,Type I Error Reject a true null hypothesis Considered a serious
14、type of error The probability of a Type I Error is Called level of significance of the test Set by researcher in advance Type II Error Failure to reject false null hypothesis The probability of a Type II Error is ,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-13,Possible Errors in H
15、ypothesis Test Decision Making,(continued),Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-14,Possible Results in Hypothesis Test Decision Making,The confidence coefficient (1-) is the probability of not rejecting H0 when it is true. The confidence level of a hypothesis test is (1-)*1
16、00%. The power of a statistical test (1-) is the probability of rejecting H0 when it is false.,(continued),Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-15,Type I otherwise do not reject H0,Basic Business Statistics, 11e 2009 Prentice-Hall, Inc.,Chap 9-21,Do not reject H0,Reject H0,Reject H0,There are two cutoff values (critical values), defining the regions of rejection,Two-Tail Tests,/2,-Z/2,0,H0: = 3 H1:
