please help with the below question using the tables given(with explanations please)

Example: If Z=1.96, then P(0-Z)=0.4750 0.4750 14.1 Normal distribution tables 0 1.96 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0. 1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 D.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3380 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3720 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4310 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0. 4505 0.4515 0.4525 0.4535 0.4545 1.7 0. 4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.F 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.0 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.499014.2 Students' t-distribution STUDENT'S f distribution PERCENTAGE POINTS df 60.0% 66.7% 75.0% 80.0 87.5% 90.0% 95.0% 97.5% 99.0% 99.5% 99.9% 0.325 0.577 1.000 1.376 2.414 3.078 6.314 12.706 31.821 63.657 318231 0.289 0.500 0.816 1.061 1.604 1.886 2.920 4.303 6.965 9.925 22.327 0.277 0.476 0.765 0.978 1.423 1.638 2.353 3.182 4.541 5.841 10.215 0.271 0.464 0.741 0.941 1.314 1.533 2.132 2.776 3.747 4.604 7.173 0.267 0.457 0.727 0.920 1.201 1.476 2.015 2.571 3.365 4.032 5.893 0.265 0.453 0.718 0.906 1.273 1.440 1.943 2.147 3.143 3.707 5.208 0.263 0.449 0.711 0.896 1.254 1.415 1.895 2.365 2.998 3.499 4.785 0.262 0.447 0.706 0.889 1.240 1.397 1.860 2.306 2.896 3.355 4.501 0.261 0.445 0.703 0.883 1.230 1.383 1.833 2.262 2.821 3.250 1.297 10 0.260 0.414 0.700 0.879 1.221 1.372 1.812 2.228 2.764 3.169 1.144 11 (.260 0.443 0.697 0.876 1.214 1.363 1.796 2.201 2.718 3.106 4.025 12 0.259 0.442 0.695 0.873 1.209 1356 1.782 2.179 2.681 3.055 3.930 0.259 0.441 0.694 0.870 1.204 1350 1.771 2.160 2.650 3.012 3.852 14 (1.258 0.440 0.692 0.868 1.200 1.345 1.761 2.145 2.624 2.977 3.787 15 0.258 0.4:39 0.691 0.866 1.197 1341 1.753 2.131 2.602 2.917 3.7353 16 0.258 0.439 0.690 0.865 1.194 1.337 1.746 2.120 2.583 2.921 3.686 17 (1257 0.438 0.689 0.863 1.191 1 333 1.740 2.110 2.567 2.898 3.646 18 (1.257 0.438 0.688 0.862 1.189 1.330 1.734 2.101 2.552 2.878 3.610 19 0.257 0.438 0.688 0.861 1.187 1.328 1.729 2.093 2.539 2.861 3.579 20 0.257 0.437 0.687 70.860 1.185 1325 1.725 2.086 2.528 2.845 3.552 21 (0.257 0.437 0.686 0.859 1.183 1.323 1.721 2080 2.518 2.831 3.527 22 0.256 0.437 0.686 0.858 1.182 1.321 1.717 2.074 2.508 2.819 3.505 0.256 0.436 0.685 0.858 1.180 1.419 1.714 2.069 2.500 2.807 3.485 24 0.256 0.436 0.685 0.857 1.179 1.318 1.711 2.064 2.192 2.797 3.467 25 0.256 0.436 0.684 0.856 1.178 1.316 1.708 2.060 2.485 2.787 3.450 26 0.256 0.436 0.684 0.856 1.177 1.315 1.706 2.056 2.479 2.779 3.4335 27 0.256 0.435 0.684 0.855 1.176 1.314 1.703 2.052 2.473 2.771 3.421 28 0.256 0.435 0.683 0.855 1.175 1313 1.701 2.048 2. 167 2.763 3.408 29 0.256 0.435 0.683 3 0.854 1.174 1.311 1.699 2.045 2. 162 2.756 3.396 30 0.256 0.435 0.683 0.854 1.173 1.310 1.697 2.042 2. 157 2.750 3.385 35 0.255 0.434 0.682 0.852 1.170 1.306 1.690 2.030 2.1:38 2.724 3.340 40 0.255 0.434 0.681 0.851 1.167 1.303 1.684 2.021 2. 123 2.704 3.307 45 0.255 0.434 0.680 0.850 1.165 1.301 1.679 2.014 2.412 2.690 3.281 50 0.255 0.433 0.679 0.849 1.164 1.299 1.676 2.009 2.403 2.678 3.261 55 0.255 0.433 0.679 0.848 1.163 1.297 1.673 2.004 2.396 2.668 3.245 60 0.254 0.433 0.679 0.848 1.162 1.296 1.671 2.000 2.390 2.660 3.232 0.254 0.433 0.667 0.846 1.158 1.291 1.662 1.987 2.:368 2.6:12 3.183 120) 0.254 0.433 0.677 0.845 1.156 1.289 1.658 1.98 2.358 2.617 3.160 (.254 0.431 0.674 0.842 1.150 1.282 1.645 1.960 2.326 2.576 3.090Executives at Toyota were given the new high-performance 3.5-litre V6 SUV automobile, they were asked to keep records of the number of miles travelled per gallon of petrol for this new vehicle using regular petrol versus high octane petrol. Their results follow. Miles per gallon High Executive Regular Octane Bowers 25 28 Smith 33 31 Grasser 31 35 Jones 45 44 King 42 47 Rau 38 40 James 29 29 Burns 42 37 Snow 41 44 Lawless 30 n Perform a dependent samples t-test (paired +-test) to examine if there is a difference in the number of miles travelled per gallon. Use a 59% significance level. (a) State the null hypothesis and the alternate hypothesis. Compute the value of the test statistic. (b) (state your answer accurate to 2 decimal places) Test Statistic t= (c) State the Degrees of Freedom? df = 9(c) State the Degrees of Freedom? df= 9 (d) Look up the critical value to (state to 3dp as given in your t-tables) t = (e) v Ho. There is evidence to indicate that there is a difference in the miles per gallon between the two types of petrol 4 reject ") sufficient or not not