Fromasampleofdatathecalculatedsamplemeanis x

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Unformatted text preview: poses that the population mean for a variable of interest exceeds the value a. Does the data support this theory ? Consider testing the null hypothesis: H0 : μ ≤ a or H0 : μ = a against the alternative hypothesis: H1 : μ > a Note the hypothesis is stated so that if the economic theory is correct the null hypothesis will be rejected. That is, there is strong evidence to support the economic theory. From a sample of data the calculated sample mean is x . If the sample mean is substantially greater than the value a then the null hypothesis can be rejected. 4 Chapter 10 When the null hypothesis is true, μ = a , and a result is: X−a ~ N(0 , 1) σ n Assume that the population standard deviation σ is known from previous research. Choose a significance level α . This sets the probability of a Type I error – rejecting a true null hypothesis. A sensible choice may be α = 0.05. From the sample of data calculate the test statistic: z= x−a σ n The decision rule is to reject the n...
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