Unit 3 -IP- Samples Essay Example | Topics and Well Written Essays - 500 words

Unit 3 -IP- Samples - Essay Example In order to test whether the two variables have the same means, a two – sample, two – sided t – test must be performed. The two - tailed test is used because the concern is not whether some variable has a larger or lower mean, but whether the two means are different. As a result, the null hypothesis was established in equation (1) below, stating that the difference in means of the two samples is random. Since the sample sizes are relatively small, the t – test is used as the preferred test (Baltagi, 2008, p.31). The confidence interval is constructed in order to test this hypothesis. The confidence set with confidence level must be determined such that the true difference of the sample means is included in this set. What this implies is that the confidence set will include the true difference of population means with probability â€Å"at least † (Paolella, 2011, p. 13), as shown in equation (3) below: The confidence level chosen is 0.95, which implies that the corresponding confidence set will contain the true population mean difference with 95% probability (Paolella, 2011, p.13). The probability of rejecting the null hypothesis when it is true is as a result 5% (Baltagi, 2008, p.21). This error is denoted as type I error. The larger the confidence interval, the larger the probability that the null hypothesis will be accepted when it is in fact false (Baltagi, 2008, p.22). This error is denoted as type II error. A t – score must be calculated by subtracting the sample means and dividing by the square root of the adjusted population variances, which can be estimated through sample variances. There are in total degree of freedom (Neustadl, n.d.). The resulting t – value is  ± 2.009, which is also the critical region (Dawson, 2012;Ruud, 2000, p.224). The t – test can be seen in equation (4) below: The t – test is preferred because of the data dependence. Both variables have in common the type of