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# lecturenotes07 - ECON 41: Statistics for Economists Lecture...

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ECON 41: Statistics for Economists Lecture Notes 0 7 Chunming Yuan [email protected] Economics Department, UCLA

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In this lecture we will consider testing hypotheses about population parameters, in particular about the population mean and proportion. In hypothesis testing, we want to know, using information from a sample, whether a given claim about a population parameter is true or not. For example we may want to know if a company’s claim that on average a can of its soda contains 12oz. of drink is true.
A null hypothesis is a claim about a population parameter that is assumed to be true until it is declared false. In the example above, the null hypothesis is H 0 : μ =12 , read as "H naught". When we test a null hypothesis we also specify an alternative hypothesis in favor of which the evidence lies if we reject the null hypothesis. For example we may want to specify the alternative hypothesis in the example above as H 1 : μ< 12 , in which case rejection of the null means that the company cheats by proclaiming that on average its sodas contain 12oz when in fact on average contain less than that.

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An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is proven false. We will distinguish between two-sided and one-sided alternatives: H 1 : μ 6 =12 :two - s ided H 1 : μ> 12 : right-sided H 1 :
Exercise 9.9: Write the null and the alternative hypotheses and determine whether each one is a two-sided, right-sided or left-sided test. The mean number of hours worked by college students is di f erent than 20 hours. A bank’s ATM is out of service for an average of 10 or more hours per month. The mean length of experience for airport security guards is di f erent from 3yea rs . The mean credit card debt of college seniors is less than \$1000.

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Naturally, we will reject the null if favor of the two-sided alternative if the realized sample value for the parameter we are interested in is either "much" smaller or "much" greater than the hypothesized value. When we are testing against a right-sided alternative it is natural to reject in favor of the alternative if the realized value is "much" greater than the hypothesized value. And when we are testing against a left-sided alternative it is natural to reject in favor of the alternative if the realized value is "much" smaller than the hypothesized value. What does much smaller or much greater mean? There are two approaches to conducting a test: the critical value and the p value approach.
In the traditional critical value approach we reject the null if the realized sample value for the parameter of interest falls in the so-called rejection or critical region. In the case of a right-sided alternative the rejection region is an interval of

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## This note was uploaded on 09/03/2009 for the course ECON 41 taught by Professor Guggenberger during the Summer '07 term at UCLA.

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lecturenotes07 - ECON 41: Statistics for Economists Lecture...

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