4.4 对单个参数进行假设检验的t检验.pdf

Example Wage equation Test whether, after controlling for education and tenure, higher work experience leads to higher hourly wages Standard errors Test against . One would either expect a positive effect of experience on hourly wage or no effect at all. Multiple Regression Analysis Inference Example Wage equation cont. The effect of experience on hourly wage is statistically greater than zero at the 5 and even at the 1 significance level. t-statistic Degrees of freedom; here the standard normal approximation applies Critical values for the 5 and the 1 significance level these are conventional significance levels. The null hypothesis is rejected because the t-statistic exceeds the critical value. Multiple Regression Analysis Inference Test against. Reject the null hypothesis in favour of the alternative hypothesis if the estimated coef- ficient is too small“ i.e. smaller than a criti- cal value. Construct the critical value so that, if the null hypothesis is true, it is rejected in, for example, 5 of the cases. In the given example, this is the point of the t- distribution with 18 degrees of freedom so that 5 of the cases are below the point. Reject if t-statistic less than -1.734 Multiple Regression Analysis Inference Testing against one-sided alternatives less than zero