Chapter 9 Review Cl

Chapter 9 Review Cl - Chapter 9 : Significance Tests about...

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Chapter 9 : Significance Tests about Hypotheses Significance tests or Tests of Hypotheses is another important method of statistical inference alongside point and interval estimation. A Hypothesis is a statement about one or more population parameters . Eg : A statement about the population mean μ may be denoted by H: u=7 (On an average, UF students studies 7 hours during the week) 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 five distinct steps viz Making Assumptions : The most important assumption is that the data result from a randomized experiment or a random sample. Other assumptions relate to sample size and shape of the population distribution. Constructing Hypothesis : Each significance test is composed of 2 hypothesis : H 0 ( Null Hypothesis) : It is a statement that specifies a particular value of the parameter determined from experience or prior belief . Ha ( Alternate Hypothesis) : It states that the population parameter falls in some alternative range of values. So, it is a statement of change. It may be one or two sided. Ex 1: Visitor records show that, during 2008, 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 Ho: u=25 and the alternative hypothesis will be Ha: u>25 Here, μ denotes the population mean number of visitors to the park per day in 2008. Here the alternative hypothesis is one sided . 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 adults has changed (for better or for worse) during recent times. So, our null hypothesis will be Ho: p=.50
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and the alternative hypothesis will be Ha: p not equal to .50 Here p is the population proportion of adults who favor legalized gambling at present. Here Ha is a two sided hypothesis. Determining the Test statistic : A test statistic measures how close the point estimate of the parameter is to the null hypothesis value(of the parameter). This “closeness” is measured in terms of the standard error of the estimate. Thus, it is given by ( Parameter estimate- null hypothesis)/ standard error Calculating the p-values : This is the probability of getting a test statistic value more extreme than what we have actually got given that the null hypothesis is true. A small p-value would indicate that our test statistic takes a value which is very unlikely under the null hypothesis. So, maybe the null hypothesis itself is (o.w our test statistic would not have been what it is). Thus, smaller p values represent stronger evidence against H 0 . Drawing conclusion
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Chapter 9 Review Cl - Chapter 9 : Significance Tests about...

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