# Hypothesis Testing

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## Hypothesis Testing

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IV. Hypothesis Testing V. Two Sided Hypothesis Testing VI. Type II Errors

- Lecture number:
- 6
- Pages:
- 2
- Type:
- Lecture Note
- School:
- Cornell University
- Course:
- Econ 3120 - Applied Econometrics
- Edition:
- 1

**Unformatted text preview: **

Econ 3120 1st Edition Lecture 6 Outline of Last Lecture I Asymptotic Normality II Central Limit Theorem III Distribution of Difference in Means Outline of Current Lecture IV Hypothesis Testing V Two Sided Hypothesis Testing VI Type II Errors Current Lecture 4 Hypothesis Testing Introduction Oftentimes we want to test whether the data are likely to be generated by a specific value or values for the true mean If we only have a random sample we cannot use sample averages i e estimates to tell us definitively whether these hypotheses are true However we can use hypothesis testing to inform whether the estimates could have been generated by particular true values We start with a null hypothesis A null hypothesis is a hypothesized value for the parameter Our null hypothesis might be that the parameter takes on a particular value This is written as H0 0 Our null could also be that the that the parameter is less than or greater than a particular value H0 0 H0 0 We then define an alternative hypothesis as hypothesized values of the parameter outside of the null This generally takes two forms First our alternative hypothesis can be any value of the parameter outside of the null HA 6 0 Our alternative could also be that the average is above or below the hypothesized value HA 0 HA 0 In a hypothesis test we can either reject or fail to reject the null hypothesis If we reject the null hypothesis we are essentially saying that it is highly unlikely that the estimate would have been generated if the null were true Essentially we need evidence against the null in order to reject If we fail to reject we are finding evidence consistent with the null hypothesis Note that failing to reject the null is not the same thing as accepting the null The most we can say is that the evidence is consistent with the null hypothesis but we cannot say with any certainty that the null is true Thus we never accept the null 4 1 Two sided hypothesis tests for the mean Suppose that we are interested in

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