**t-Distribution Table Explanation**This educational page includes a table for the t-distribution, which is commonly used in statistics to determine critical values for hypothesis testing. The table provides the t-scores corresponding to different right-tail probability values for various degrees of freedom (df).**Diagram:**- **Plot:** The diagram at the top-left shows the standard distribution curve with the right-tail area shaded. This visualizes how the t-score relates to statistical significance, with the shaded region representing the probability or alpha level.**Table VI: t-Distribution Areas**The table lists t-scores associated with specific alpha levels (areas in the right tail). It has the following components:- **Degrees of Freedom (df):** Listed in the far-left column, ranging from 1 to 100, plus additional values like 1000 and infinity, which are typical for large-sample approximations.- **Columns:** Each column corresponds to a different significance level (alpha value) for the right-tail area: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005.- **Entries:** Each entry under these columns provides the critical t-value for the given degrees of freedom and significance level. These values are used to determine whether to reject the null hypothesis in statistical testing.**How to Use the Table:**1. **Identify the Degrees of Freedom (df):** Based on your sample size (n), calculate df as n - 1. 2. **Select Significance Level:** Determine the significance level (alpha) you’re testing against. Commonly used levels are 0.05, 0.01, etc.3. **Find the Critical Value:** Locate the row corresponding to your df and move across to the column for your alpha level to find the critical t-value.This table is essential for conducting t-tests and confidence interval calculations in statistical analyses. **Transcription:**A simple random sample of size \( n \) is drawn. The sample mean, \(\overline{x}\), is found to be 18.4, and the sample standard deviation, \( s \), is found to be 4.8.

We are going to find the 95% confidence interval by finding the critical value

A- Area in right tail Table VI t-Distribution Area in Right Tail 0.025 0.01 0.005 0.0025 15.894 31.821 63.657 12.706 127.321 4.303 4.849 6.965 9.925 14.089 3.182 3.482 4.541 5.841 7.453 2.776 2.999 3.747 4.604 5.598 2.571 3.365 4.032 4.773 2.757 2.612 3.143 3.707 2.447 2.998 3.499 2.365 2.306 2.262 2.398 2.821 2.517 2.449 2.896 3.355 3.250 2.359 2.764 3.169 2.583 2.228 0.697 0.876 1.088 1.363 1.796 2.201 0.695 0.873 1.083 1.356 1.782 2.179 0.694 0.870 1.079 1.350 1.771 2.160 0.692 0.868 1.076 1.345 1.761 2.145 2.264 0.691 0.866 1.074 1.341 1.753 2.131 2.249 0.690 0.865 1.071 1.337 1.746 2.120 2.235 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 0.688 0.862 1.067 1.330 1.734 2.101 0.688 0.861 1.066 1.328 1.729 2.093 0.687 0.860 1.064 1.325 1.725 2.086 0.686 0.859 1.063 1.323 1.721 2.080 0.686 0.858 1.061 1.321 1.717 2.074 0.685 0.858 1.060 1.319 1.714 2.069 0.685 0.857 1.059 1.318 1.711 2.064 0.684 0.856 1.058 2.214 2.552 2.189 2.518 2.183 2.508 2.177 2.500 2.807 2.172 2.492 2.797 2.060 2.167 2.485 2.787 1.316 1.708 0.684 0.856 1.058 1.315 1.706 2.162 2.479 2.779 2.473 2.771 2.738 2:000 2.056 0.684 0.855 1.057 1.314 1.703 2.052 2.158 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 0.681 0.851 2.733 1.050 1.303 1.684 2.021 0.25 0.20 0.15 0.10 0.05 1.000 1.376 1.963 3.078 6.314 0.816 1.061 1.386 1.886 2.920 0.765 0.978 1.250 1.638 2.353 0.741 0.941 1.190 1.533 2.132 0.727 0.920 1.156 1.476 2.015 0.718 0.906 1.134 1.440 1.943 0.711 0.896 1.119 1.415 1.895 0.706 0.889 1.108 1.397 1.860 0.703 0.883 1.100 1.383 1.833 0.700 0.879 1.093 1.372 1.812 0.02 2.328 2.718 3.106 3.055 2.303 2.681 2.282 2.650 3.012 2.624 2.977 2.602 2.947 2.921 2.898 2.878 2.205 2.539 2.861 2.197 2.528 2.845 2.831 2.819 2.728 2.724 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.067 3.057 3.047 3.038 3.030 3.022 3.015 3.008 3.002 2.996 3.527 3.505 3.104 3.485 3.091 3.467 3.078 3.450 2.719 2.990 2.985 0.001 2.980 2.976 2.123 2.423 2.704 2.971 318.309 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.435 3.421 3.408 3.396 3.385 3.375 3.365 3.356 3.348 3.340 3.333 3.326 3.319 3.313 3.307 0.0005 636.619 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.633 3.622 3.611 3.601 3.591 3.582 3.574 3.566 3.558 3.551