Chapter 8 Review - Chapter 8 : Significance Tests about...

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Chapter 8 : Significance Tests about Hypotheses Significance tests or Tests of Hypotheses is another major method of statistical inference alongside point and interval estimation. A Hypothesis is a statement about one or more . Eg : A statement about the population mean μ may be denoted by . A Significance test is a method by which it is decided whether the above statement about the parameter is supported by the data observed from a random sample. Any significance test has distinct steps viz Making Assumptions : The most important assumption is that the data result from a randomized experiment or a . Other assumptions relate to and of the population distribution. Constructing Hypothesis : Each significance test has two hypothesis : H 0 ( Hypothesis) : It is a statement that specifies a particular value of the parameter
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determined from or . Ha ( Hypothesis) : It states that the population parameter falls in some alternate range of values. So, it is a statement of change. It may be or sided. Ex 1: Visitor records show that, during 2006, on an average, about 25 visitors visited Kanapaha Botanical gardens per day. Since then some beautification has been done and the park management suspects that the number of visitors may have increased. Thus, our null hypothesis will be and the alternative hypothesis will be Here, μ denotes the population mean number of visitors to the park per day in 2007. Here the alternative hypothesis is . Eg 2 : Historically in Canada, the proportion of adults who favour legalized gambling has been 0.50. The government wants to know whether the mindset of
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adults has changed (for better or for worse) during recent times. So, our null hypothesis will be and the alternative hypothesis will be Here p is the of adults who favor legalized gambling at present. Here Ha is a hypothesis. Note : In practice, two sided tests are more common than one-sided tests. Determining the Test statistic : A test statistic measures how the of the parameter is to the value(of the parameter). This “closeness” is measured in terms of the of the estimate. Thus, it is given by Calculating the p-values : This is the probability that the test statistic equals its observed value or more
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is true. A p-value would indicate that our test statistic takes a value which is very under the hypothesis. So, maybe the null hypothesis itself is (o.w our test statistic would not have taken the value it has taken). Thus, p values represent evidence against H 0 . Drawing conclusion : We make a decision about whether to “reject” or “not to reject” H 0 by comparing the p-value and the (usually 0.05). A would lead to the of Significance level tells us how strong the evidence should be for us to reject H 0 . Eg :
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This note was uploaded on 04/18/2008 for the course EXP 3116 taught by Professor Fasig during the Spring '08 term at University of Florida.

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Chapter 8 Review - Chapter 8 : Significance Tests about...

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