One Sided Tests, Confidence Intervals (2 pages)

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One Sided Tests, Confidence Intervals



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One Sided Tests, Confidence Intervals

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II. One Sided Tests III. Confidence Intervals


Lecture number:
7
Pages:
2
Type:
Lecture Note
School:
Cornell University
Course:
Econ 3120 - Applied Econometrics
Edition:
1

Unformatted text preview:

Econ 3120 1st Edition Lecture 7 Outline of Last Lecture I No Class Outline of Current Lecture II One Sided Tests III Confidence Intervals Current Lecture III 2 One sided tests of the mean Sometimes we are interested in testing against a one sided alternative That is our alternative hypothesis is that the true value is greater than the null H0 0 HA 0 or HA 0 If we are conducting a one sided test we will only reject the null if the test statistic is on one side of the hypothesized distribution For example if our alternative is HA 0 then we will only reject if our sample mean Y is very large In this case we could also state our null as H0 0 This is equivalent to H0 0 because the we reject when 0 in either case For one sided tests the critical values will be lower in absolute value than the critical values for two sided tests at the same confidence level This occurs because we only find evidence against H0 and in favor of HA when our test statistic is on one side of the distribution For HA 0 we reject when our test statistic is large enough such that it only would have been generated 100 of the time We therefore reject if t c where c is chosen such that P Tn 1 c H0 1 III 3 Testing differences in means or equality of two different means We might be interested in whether means of two populations are equal or if their difference equals some value We can test differences in means in a similar way that we test single means In this case our null hypothesis would be H0 x y 4 0 If 4 0 0 then we are testing equality of means H0 x y We saw in earlier that regardless of the population distributions t q X Y 4 0 s 2 x n1 s 2 y n2 III 4 has an asymptotic standard normal distribution 3 Therefore we can test the difference in means in the same manner that we would a single mean Example The same poll as above found that 49 of those under 35 and 44 of those over 65 approve of Obama If 250 of each group were surveyed test whether the true difference is 0 at the 5 level against a two sided



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