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Stock - M. Watson, Introduzione all'Econometria, Pearson. Education Italia, Stock J. Analisi dei dati con R ; Il corso intende fornire un'introduzione all'utilizzo di R, presentando le The central limit theorem suggests that when the sample size n is large, the distribution of the. The second equality uses the fact that 1 Y , …, Yn are i. Part d is a one-sided test and the p -value is the area under the standard normal distribution to the right of the calculated t -statistic.
The p -value 0. Equivalently the calculated t -statistic 1 The test suggests that the survey did not contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey.
Note that the largest value that. Thus if 2. Thus the null hypothesis 0. Denote the life of a light bulb from the new process by. Y is the sample mean with a sample size We calculate first the probability of the manager erroneously accepting the null hypothesis when it is invalid:. From part b the standard error of the difference in the two sample means is SE 1 2 1 The t -statistic for testing the null hypothesis is. Because of the extremely low p -value, we can reject the null hypothesis with a very high degree of confidence.
That is, the population means for Iowa and New Jersey students are different. Assume that n is an even number.
Use Equation 3. The extremely low level of p -value implies that the difference in the monthly salaries for men and women is statistically significant. We can reject the null hypothesis with a high degree of confidence. To examine whether there is gender discrimination in the compensation policies, we take the following one-sided alternative test.
With the extremely small p -value, the null hypothesis can be rejected with a high degree of confidence. There is overwhelming statistical evidence that mean earnings for men are greater than mean earnings for women. However, by itself, this does not imply gender discrimination by the firm.
Gender discrimination means that two workers, identical in every way but gender, are paid different wages. The data description suggests that some care has been taken to make sure that workers with similar jobs are being compared. But, it is also important to control for characteristics of the workers that may affect their productivity education, years of experience, etc.
If these characteristics are systematically different between men and women, then they may be responsible for the difference in mean wages.
If this is true, it raises an interesting and important question of why women tend to have less education or less experience than men, but that is a question about something other than gender discrimination by this firm.
Since these characteristics are not controlled for in the statistical analysis, it is premature to reach a conclusion about gender discrimination. The standard error of Y is SE 19 5. The p -value for the one-sided test is: With the small p -value, the null hypothesis can be rejected with a high degree of confidence.
There is statistically significant evidence that the districts with smaller classes have higher average test scores. We have the following relations: Randomly select one half. Administer the test again to all of the n students. Compare the gain in performance of the prep-course second-time test takers to the non-prep-course second-time test takers.
Because X and Y have finite fourth moments, the second moment of Wi is finite,. Thus, standard deviation is 2 11 5. Suppose the regression.
The standard error of the regression is. It determines the overall level of the line. Thus SER is measures in dollars per week. The oldest worker in the sample is 65 years old. The distribution of earning is positively skewed and has kurtosis larger than the normal. Using the expression in a. Some students will have studied more than average, other less; some students will have higher than average aptitude for the subject, others lower, and so forth.
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