Construct and interpret a Confidence Interval to estimate an entire population's Mean The grade point averages for 10 randomly selected college students are listed here: 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 Assume grade point averages are normally distributed (that is, have a Normal/Bell-shaped distribution). (a) Find a point estimate X for the population mean. (b) Find the Margin of Error for a 98% confidence interval. You must use the correct critical value from Table VII. (c) Construct a 98% confidence interval for the population mean. (d) Interpret the confidence interval, "We are 98% confident that ...." Table VII 1-Distribution Area in Right Tail 0.10 0.02 0.01 0.005 0.0025 0.001 0.000! 0.25 0.20 0.15 987 318.309 636.614 1.000 1.376 1.963 3.078 6314 12.706 15.894 31.821 63.657 127.321 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.591 12.92 0.765 0.978 1.250 1.638 2 353 3.182 3.482 4.541 5.841 7.453 10.215 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.611 0.741 2.757 3.36 4.032 4.773 5.893 5.86' 0.727 0.920 1.156 1.476 2.015 2.571 1.440 5.208 5.95 0.718 0.906 1.134 1.943 2.447 2.612 3.143 3.707 4.317 3.499 4.029 4.785 5.40: 0.71 0.896 1.119 1.415 1.895 2.365 2.517 2.998 4.501 5.04 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.83 3.250 3.690 4.297 4.78 0.70 0.883 1.100 1.38 1.833 2 262 2.398 2.821 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.58 4.144 4.58 3.497 4.02 4.43 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.428 3.930 4.31 12 0.695 1.083 1.356 1.782 2.179 2.303 2.681 3.055 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.22 4.14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.07 0.691 0.866 1.074 1.34 1.753 2.131 2.249 2.602 2.947 3.286 3.733 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2583 2921 3.252 3.686 4.01 2.567 2.898 3.222 3.646 3.96 0.689 0.863 1.069 1.333 1.740 2.110 2.224 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2552 2.878 3.197 3.610 3.92 3.579 3.88 19 0.688 0.861 1.328 1.729 2.093 2 539 3.174 1.066 2.205 2861 3.552 3.85 20 0.68 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2518 2 831 3.135 3.527 3.81 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2 508 2819 3.119 3.505 3.75 0.685 0.858 1.060 1.319 1.714 2.065 2.177 2.500 2.807 3.104 3.485 3.76 A IM 1 707 a nal 1 467 3.74