Please help by providing detailed calculations and answers.
Use the tables provided.
Table II Normal Curve Areas 0 Z N .00 .01 .02 03 .04 .05 .06 07 .08 09 .0000 0040 .0080 0120 .0160 0199 .0239 0279 .0319 0359 .0398 .0438 .0478 0517 .0557 0596 .0636 0675 .0714 .0793 0753 .0832 .0871 0910 0948 0987 .1026 1064 .1179 .1103 .1217 .1141 .1255 .1293 .1331 .1368 .1406 1443 .1554 .1480 .1591 .1517 .1628 .1664 1700 .1736 .1772 .1808 .1844 .1915 1879 .1950 .1985 2019 .2054 .2088 .2123 .2157 .2190 .2224 .2257 2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 .2881 .2823 .2852 .2910 .2939 .2967 .2995 3023 .3051 3078 .3159 .3133 3186 .3106 .3212 .3238 .3264 3289 .3315 .3340 .3365 3389 .3413 .3438 .3461 .3485 .3508 3531 .3554 .3577 .3599 3621 .3643 .3665 .3686 3708 .3729 .3749 3770 .3790 .3810 3830 .3849 3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 4015 4032 .4049 4066 4082 4099 4115 .4131 4147 1.4 4162 4177 .4192 4207 4222 4236 1.5 4251 4265 .4279 4292 .4306 .4332 .4319 4345 4357 .4370 4382 4394 .4406 4418 .4429 4441 1.6 .4452 .4463 .4474 .4484 .4495 4505 .4515 1.7 4525 4535 4545 .4554 .4564 .4573 4582 .4591 4599 1.8 .4608 .4616 4625 .4633 .4641 .4649 .4656 .4664 .4671 .4678 1.9 .4686 .4713 .4693 4699 .4719 .4726 .4706 4732 .4738 .4744 2.0 .4750 4756 .4772 4761 .4767 4778 4783 4788 4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 4830 .4834 4838 .4842 4846 .4850 2.2 4854 .4857 4861 4864 4868 4871 4875 .4878 4881 .4884 2.3 4887 4890 4893 4896 4898 4901 4904 .4906 4909 2.4 .4911 4913 4916 4918 4920 .4922 4925 .4927 .4929 2.5 4931 .4932 4934 .4936 .4938 .4940 .4941 .4943 4945 4946 .4948 .4949 4951 .4952 2.6 .4953 .4955 4956 4957 4959 .4960 4961 4962 2.7 4963 4965 4964 .4966 4967 4968 4969 .4970 .4971 4972 .4973 2.8 .4974 4974 4975 4976 4977 .4977 4978 .4979 4979 4980 4981 2.9 4981 4982 4982 4983 .4984 4984 .4985 .4985 4986 3.0 4986 .4987 4987 4987 4988 .4988 4989 .4989 4989 4990 4990In a recent study, the strengths of a plywood and oriental strand brand (053) were compared. Independent random samples of each type of wood were obtained, and the dry density of each piece {inkg 'i m ) was measured. Assume that populations are normal and the variances are equal. The summary statistics are given in the following table: =53L8 .5" =5.5o =005.1 .r: =723 Ph'it'nm! n. =I 2 a 058 n: :15 f: a. Find a 99% confidence interval for the difference in population mean dry densities. b. Interpret the interval found in part a. c. Do the data indicate that the true mean dry density of plywood is signicantly less than the true mean dry density of 0313? Us = 0-05- (E) State the null and alternative hypotheses. (ii) Calculate the value of the test statistic. (iii) Rejection region. (iv) Conclusion. (vi) What assumption are necessary for the test in part c to be valid? a 0 Degrees of Freedom 100 t.050 1 025 1010 1 005 1001 t.0005 3.078 6.314 12.706 31.821 63.657 318.31 636.62 1.886 2.920 4.303 6.965 9.925 22.326 31.598 1.638 2.353 3.182 4.541 5.841 10.213 12.924 1.533 2.132 2.776 3.747 4.604 7.173 8.610 1.476 2.015 2.571 3.365 4.032 5.893 6.869 1.440 1.943 2.447 3.143 3.707 5.208 5.959 1.415 1.895 2.365 2.998 3.499 4.785 5.408 1.397 1.860 2.306 2.896 3.355 4.501 5.041 1.383 1.833 2.262 2.82 3.250 4.297 4.781 1.372 1.812 2.228 2.764 3.169 4.144 4.587 1.363 1.796 2.201 2.718 3.106 4.025 4.437 1.356 1.782 2.179 2.681 3.055 3.930 4.318 1.350 1.771 2.160 2.650 3.012 3.852 4.221 1.345 1.761 2.145 2.624 2.977 3.787 4.140 1.341 1.753 2.131 2.602 2.947 3.733 4.073 1.337 1.746 2.120 2.583 2.921 3.686 4.015 1.333 1.740 2.110 2.567 2.898 3.646 3.965 1.330 1.734 2.101 2.552 2.878 3.610 3.922 1.328 1.729 2.093 2.539 2.861 3.579 3.883 1.325 1.725 2.086 2.528 2.845 3.552 3.850 1.323 1.721 2.080 2.518 2.831 3.527 3.819 1.321 1.717 2.074 2.508 2.819 3.505 3.792 1.319 1.714 2.069 2.500 2.807 3.485 3.767 1.318 1.711 2.064 2.492 2.797 3.467 3.745 1.316 1.708 2.060 2.485 2.787 3.450 3.725 1.315 1.706 2.056 2.479 2.779 3.435 3.707 1.314 1.703 2.052 2.473 2.771 3.421 3.690 1.313 1.701 2.048 2.467 2.763 3.408 3.674 1.311 1.699 2.045 2.462 2.756 3.396 3.659 1.310 1.697 2.042 2.457 2.750 3.385 3.646 1.303 1.684 2.021 2.423 2.704 3.307 3.551 1.296 1.671 2.000 2.390 2.660 3.232 3.460 1.289 1.658 1.980 2.358 2.617 3.160 3.373
