1. no work needed, only the correct solution:

A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 6 cars has a mean gas mileage of 22 mpg and a standard deviation of 4 mpg. At a = 0.05, test the company's claim. Assume the population is normally distributed. Click here to view the t-distribution table. Click here to view page 1 of the normal table. Click here to view page 2 of the normal table. TTT Which sampling distribution should be used and why? O A. Use a normal sampling distribution because the population is normal, and a is known. O B. Use a t-sampling distribution because n 30. OF. Use a normal sampling distribution because the population is normal, and o is unknown. State the appropriate hypotheses to test. O A. Ho: HS 23 B. Ho: H 2 23 HA: [ > 23 Ha: u O 2 02 E St-Distribution Table Level of confidence, c 0.80 0.90 0.95 0.98 0.99 One tail, or 0.10 0.05 0.025 0.01 0.005 d.f. Two tails, or 0.20 0.10 0.05 0.02 0.01 d.f. 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 1.638 2.353 3.182 4.541 5.841 1.533 2.132 2.776 3.747 4.604 1.476 2.015 2.571 3.365 4.032 1.440 1.943 2.447 3.143 3.707 6 1.415 1.895 2.365 2.998 3.499 7 1.397 1.860 2.306 2.896 3.355 1.383 1.833 2.262 2.821 3.250 9 1.372 1.812 2.228 2.764 3.169 10 1.363 1.796 2.201 2.718 3.106 11 1.356 1.782 2.179 2.681 3.055 12 13 1.350 1.771 2.160 2.650 3.012 13 14 1.345 1.761 2.145 2.624 2.977 14 15 1.341 1.753 2.131 2.602 2.947 15 16 1.337 1.746 2.120 2.583 2.921 16 17 1.333 1.740 2.110 2.567 2.898 17 18 1.330 1.734 2.101 2.552 2.878 18 19 1.328 1.729 2.093 2.539 2.861 19 20 1.325 1.725 2.086 2.528 2.845 20 21 1.323 1.721 2.080 2.518 2.831 21 22 1.321 1.717 2.074 2.508 2.819 22 23 1.319 1.714 2.069 2.500 2.807 23 24 1.318 1.711 2.064 2.492 2.797 24 25 1.316 1.708 2.060 2.485 2.787 25 26 1.315 1.706 2.056 2.479 2.779 26 27 1.314 1.703 2.052 2.473 2.771 27 28 1.313 1.701 2.048 2.467 2.763 28 29 1.311 1.699 2.045 2.462 2.756 29 30 1.310 1.697 2.042 2.457 2.750 30 31 1.309 1.696 2.040 2.453 2.744 31 32 1.309 1.694 2.037 2.449 2.738 32 33 1.308 1.692 2.035 2.445 2.733 33 34 1.307 1.691 2.032 2.441 2.728 34 35 1.306 1.690 2.030 2.438 2.724 35 36 1.306 1.688 2.028 2.434 2.719 36 37 1.305 1.687 2.026 2.431 2.715 37 38 1.304 1.686 2.024 2.429 2.712 38 39 1.304 1.685 2.023 2.426 2.708 39 40 1.303 1.684 2.021 2.423 2.704 40 45 1.301 1.679 2.014 2.412 2.690 45 50 1.299 1.676 2.009 2.403 2.678 50 60 1.296 1.671 2.000 2.390 2.660 60 70 1.294 1.667 1.994 2.381 2.648 70 80 1.292 1.664 1.990 2.374 2.639 80 90 1.291 1.662 1.987 2.368 2.632 90 100 1.290 1.660 1.984 2.364 2.626 100 500 1.283 1.648 1.965 2.334 2.586 500 1000 1.282 1.646 1.962 2.330 2.581 1000 1.282 1.645 1.960 2.326 2.576Area under a normal curve to the left of z (page 1) .08 .07 .06 .05 04 .03 .02 .01 .00 -3.4 0002 0003 0003 0003 0003 0003 0003 0003 0003 -3.4 -3.3 0003 0004 0004 0004 0004 0004 0004 0005 DO05 0005 -3.3 -3.2 .0005 0005 .0005 10006 0006 0006 0006 0006 0007 0007 -3.2 - 3.1 0007 0007 0008 10008 0008 0008 0009 0009 0009 0010 -3.1 -3.0 0010 0010 0011 0011 0011 0012 0012 0013 0013 0013 -3.0 -2.9 0014 0014 0015 0015 0016 0016 0017 0018 0018 0019 -2.9 - 2.8 0019 0020 0021 0021 0022 0023 0023 0024 0025 0026 -2.8 -2.7 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 -2.7 -2.6 0036 0037 0038 0039 0040 0041 0043 0044 0045 .0047 -2.6 - 2.5 0048 0049 0051 0052 0054 0055 0057 0059 0060 0062 -2.5 -2.4 0064 0066 0068 0069 0071 0073 0075 0078 0080 0082 -2.4 -2.3 0084 0087 0089 0091 0094 0096 0099 0102 0104 0107 -2.3 -2.2 0110 0113 0116 0119 0122 0125 0129 .0132 0136 0139 -2.2 -2.1 0143 0146 0150 0154 0158 0162 0166 0170 0174 0179 -2.1 -2.0 0183 0188 0192 0197 0202 0207 0212 0217 0222 0228 -2.0 - 1.9 0233 0239 0244 0250 0256 0262 0268 0274 0281 0287 -1.9 -1.8 0294 0301 0307 0314 0322 0329 0336 0344 0351 0359 -1.8 -1.7 0367 0375 0384 0392 0401 0409 0418 0427 .0436 0416 -1.7 -1.6 0455 0465 0475 0485 0495 0505 0516 0526 .0537 0548 -1.6 -1.5 0559 0571 0582 .0594 0606 0618 0630 0643 0655 0668 -1.5 -1.4 0681 0694 0708 0721 0735 0749 0764 0778 0793 .0808 -1.4 -1.3 0823 0838 0853 0869 0885 0901 0918 0934 0951 0968 -13 - 1.2 0985 1003 1020 1038 1056 1075 1093 1112 1131 1151 -1.2 -1.1 .1170 .1190 1210 .1230 1251 1271 .1292 1314 1335 .1357 -1.1 -1.0 .1379 -1401 1423 .1446 -1469 1492 .1515 .1539 1562 .1587 -1.0 -0.9 .1611 1635 .1660 .1685 -1711 .1736 .1762 .1788 .1814 1841 -0.9 -0.8 .1867 1894 .1922 -1949 1977 2005 2033 2061 .2090 2119 - 0.8 - OT 2148 2177 2206 2236 2266 2296 2327 2358 2389 2420 -0.7 - 0.6 2451 2483 2514 2546 2578 2611 2643 2676 2709 2743 -0.6 - 0.5 2776 2810 2843 2877 2912 2946 2981 3015 3050 3085 -0.5 - 0.4 3121 3156 3192 3228 3264 3300 3336 3372 3409 3446 -0.4 - 0.3 3483 3520 3557 3594 3632 3669 3707 3745 3783 3821 - 0.3 - 0.2 3859 3897 3936 3974 4013 4052 4090 4129 4168 4207 - 0.2 -0.1 4247 4286 4325 4364 4404 4443 4483 4522 4562 4602 -0.1 -0.0 4641 4681 4721 4761 4801 4840 4880 4920 4960 5000 -0.0 .09 08 07 06 05 04 03 02 .01 .00Area under a normal curve to the left of z (page 2) E 00 01 02 .03 04 .05 .06 07 .09 0.0 5000 .5040 5080 5120 5160 5199 5239 5279 5319 5359 0.0 0.1 5398 .5438 5478 5517 5557 5596 5636 5675 5714 5753 0.1 0.2 5793 .5832 5871 5910 5948 5987 6026 6064 6103 6141 0.2 0.3 6179 6217 6255 6293 6331 6368 6406 6443 6480 6517 0.3 6554 6591 6628 6664 6700 6736 6772 6808 684 6879 0.4 0.5 6915 .6950 6985 7019 7054 7088 7123 .7157 7190 .7224 0.5 0.6 7257 .7291 7324 .7357 .7389 7422 .7454 .7486 7517 .7549 0.6 0.7 7580 .7611 7642 .7673 7704 .7734 7764 7794 7823 .7852 0.7 0.8 7881 .7910 .7939 .7967 .7995 8023 .8051 8078 8106 8133 0.8 0.9 8159 .8186 8212 8238 8264 8289 8315 8340 8365 .8389 0.9 1.0 8413 .8438 8461 8485 8508 8531 .8554 8577 8599 8621 1.0 1.1 8613 8665 8686 8708 8729 8749 8770 8790 8810 8830 1.1 1.2 8849 8869 8888 8907 8925 8944 8962 8980 8997 9015 1.2 1.3 9032 9049 9066 9082 9099 9115 9131 9147 9162 9177 1.3 1.4 9192 9207 9222 9236 9251 9265 9279 .9292 9306 9319 1.4 1.5 9332 .9345 9357 9370 9382 9394 .9406 9418 9429 .9441 1.5 1.6 9452 .9463 9474 .9484 9495 9505 .9515 .9525 .9535 .9545 1.6 1.7 9554 9564 9573 .9582 9591 .9599 .9608 9616 9625 .9633 1.7 1.8 9641 .9649 9656 9664 9671 9678 .9686 .9693 9695 9706 1.8 1.9 9713 .9719 9726 9732 9738 9744 9750 9756 9761 9767 1.9 2.0 9772 9778 9783 9788 9793 9798 9803 9808 9812 9817 2.0 2.1 9821 9826 9830 .9834 9838 9842 9846 9850 9854 9857 2.1 2.2 9861 9864 9868 9871 9875 9878 988 9884 9887 9890 2.2 2.3 .9893 .9896 9898 9901 9904 9906 .9909 9911 9913 9916 2.3 2.4 9918 .9920 9922 9925 9927 .9929 .9931 9932 .9934 .9936 2.4 2.5 9938 9940 9941 9943 9945 .9946 9948 9949 9951 9952 2.5 2.6 9953 .9955 9956 .9957 .9959 9960 9961 9962 .9963 .9964 2.6 2.7 9965 .9966 3967 9968 9969 9970 .9971 9972 9973 9974 2.7 2.8 9974 9975 9976 9977 9977 9978 .9979 9979 9980 9981 2.8 2.9 9981 9982 9982 9983 9984 9984 9985 9985 9986 9986 2.9 9987 9987 9987 9988 9988 9989 9989 9989 9990 9990 3.0 3.1 9990 999 9991 9991 9992 9992 9997 9992 .9993 .9993 3.1 3.2 9993 .9993 9994 9994 9994 9994 9994 .9995 9995 9995 3.7 3.3 9995 9995 9995 9996 9996 9996 9996 9996 9996 9997 3.3 3.4 9997 9997 9997 .9997 9997 .9997 9997 9997 .9997 9998 3.4 .01 .02 03 .04 05 .06 07 08 .09