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The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20. a) What is the point estimate of the population mean? b) With 90% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the population mean?

The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20. a) What is the point estimate of the population mean? b) With 90% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the population mean?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q4) The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20.

a) What is the point estimate of the population mean?

b) With 90% confidence, what is the margin of error?

c) What is the 95% confidence interval estimate of the population mean?

d) Calculate good samples and bad samples and show the area of these two samples using a curve based on finding c).

e) Write a summary based on your answer of c)

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative probability Entries in the table give the area under the curve to the left of the z value. For example, for z = 1.25, the cumulative probability is .8944. .00 .01 .02 .03 .04 .05 .06 .07 .08 09 5040 .5080 .5120 .5199 .5596 .0 5000 .5160 .5239 .5279 5319 5359 5438 .5832 .5478 .5871 .5557 .5948 .6331 .1 5398 .5517 5636 .5675 .5714 5753 .2 .3 5910 .6293 .6664 .5793 $987 .6368 .6736 .6026 .6064 .6443 6103 .6141 .6217 .6591 .6179 .6255 .6628 .6406 .6480 .6517 .4 .6554 .6700 .6772 .6808 .6844 .6879 .5 .7088 .6950 .7291 .7611 .6915 .6985 .7019 .7054 .7123 .7157 .7190 4כרה .7357 .7673 .7967 ,7389 .7486 .7794 .6 .7257 .7580 .7881 .7324 .7422 .7454 .7517 .7549 .7 .7823 .8106 .8365 .7642 .7704 .7734 .7764 .7852 .7910 .7939 7995 .8078 .8340 .8 8023 8051 8133 .9 8159 .8186 .8212 .8238 .8264 .8289 .8315 8389 .8413 .8643 .8849 .8438 .8665 .8869 .8485 .8708 1.0 .8461 8554 .8508 .8729 .8925 .8531 .8577 .8599 8621 1.1 .8686 .8888 .8749 8770 .8790 .8810 .8830 1.2 .8907 .8944 .8962 .8980 .8997 .9032 .9192 .9049 .9207 9099 9251 9115 9265 9131 9279 .9162 9306 .9015 9177 9319 1.3 .9066 .9082 9147 1.4 .9222 9236 9292 .9345 .9357 9474 1.5 .9332 .9370 .9484 .9582 .9382 9406 .9429 .9535 .9625 9441 .9545 .9394 .9418 .9525 .9616 .9693 L6 .9452 9505 9515 9463 .9564 9649 9495 9554 .9641 1.9 1.7 .9573 9591 9599 .9608 9633 1.8 .9656 .9664 .9671 .9678 .9686 9699 9706 .9713 .9719 .9726 .9732 .9738 .9744 9750 .9756 9761 .9767 .9783 .9788 .9793 9838 .9798 9842 .9803 .9846 9808 .9812 .9854 2.0 כ977. .9778 .9817 .9857 .9890 2.1 .9821 .9826 9830 9834 9850 2.2 9875 .9904 .9861 .9864 .9868 .9871 .9878 .9881 .9884 9887 .9893 .9918 2.3 .9896 .9898 .9901 .9906 .9911 .9913 .9934 .9909 .9916 2.4 9920 .9922 .9925 .9927 .9929 .9931 9932 9936 .9940 .9943 .9945 9959 .9969 .9946 9960 .9970 2.5 .9938 9953 .9941 .9951 9963 .9948 .9949 .9952 2.6 9955 9956 9957 .9968 .9961 .9962 .9964 9965 .9974 .9967 .9976 2.7 .9972 .9979 .9973 .9980 9966 .9971 .9974 2.8 .9975 .9977 .9977 .9978 .9979 .9981 2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 9990 .9990
Transcribed Image Text:CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative probability Entries in the table give the area under the curve to the left of the z value. For example, for z = 1.25, the cumulative probability is .8944. .00 .01 .02 .03 .04 .05 .06 .07 .08 09 5040 .5080 .5120 .5199 .5596 .0 5000 .5160 .5239 .5279 5319 5359 5438 .5832 .5478 .5871 .5557 .5948 .6331 .1 5398 .5517 5636 .5675 .5714 5753 .2 .3 5910 .6293 .6664 .5793 $987 .6368 .6736 .6026 .6064 .6443 6103 .6141 .6217 .6591 .6179 .6255 .6628 .6406 .6480 .6517 .4 .6554 .6700 .6772 .6808 .6844 .6879 .5 .7088 .6950 .7291 .7611 .6915 .6985 .7019 .7054 .7123 .7157 .7190 4כרה .7357 .7673 .7967 ,7389 .7486 .7794 .6 .7257 .7580 .7881 .7324 .7422 .7454 .7517 .7549 .7 .7823 .8106 .8365 .7642 .7704 .7734 .7764 .7852 .7910 .7939 7995 .8078 .8340 .8 8023 8051 8133 .9 8159 .8186 .8212 .8238 .8264 .8289 .8315 8389 .8413 .8643 .8849 .8438 .8665 .8869 .8485 .8708 1.0 .8461 8554 .8508 .8729 .8925 .8531 .8577 .8599 8621 1.1 .8686 .8888 .8749 8770 .8790 .8810 .8830 1.2 .8907 .8944 .8962 .8980 .8997 .9032 .9192 .9049 .9207 9099 9251 9115 9265 9131 9279 .9162 9306 .9015 9177 9319 1.3 .9066 .9082 9147 1.4 .9222 9236 9292 .9345 .9357 9474 1.5 .9332 .9370 .9484 .9582 .9382 9406 .9429 .9535 .9625 9441 .9545 .9394 .9418 .9525 .9616 .9693 L6 .9452 9505 9515 9463 .9564 9649 9495 9554 .9641 1.9 1.7 .9573 9591 9599 .9608 9633 1.8 .9656 .9664 .9671 .9678 .9686 9699 9706 .9713 .9719 .9726 .9732 .9738 .9744 9750 .9756 9761 .9767 .9783 .9788 .9793 9838 .9798 9842 .9803 .9846 9808 .9812 .9854 2.0 כ977. .9778 .9817 .9857 .9890 2.1 .9821 .9826 9830 9834 9850 2.2 9875 .9904 .9861 .9864 .9868 .9871 .9878 .9881 .9884 9887 .9893 .9918 2.3 .9896 .9898 .9901 .9906 .9911 .9913 .9934 .9909 .9916 2.4 9920 .9922 .9925 .9927 .9929 .9931 9932 9936 .9940 .9943 .9945 9959 .9969 .9946 9960 .9970 2.5 .9938 9953 .9941 .9951 9963 .9948 .9949 .9952 2.6 9955 9956 9957 .9968 .9961 .9962 .9964 9965 .9974 .9967 .9976 2.7 .9972 .9979 .9973 .9980 9966 .9971 .9974 2.8 .9975 .9977 .9977 .9978 .9979 .9981 2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 9990 .9990
Table entry for p and C is the critical value t with probability p lying to its right and probability C lying between -t' and t'. Probability p TABLE D t distribution critical values Upper-tail probability p dí .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 0005 1.000 1.376 1.061 0.978 1.963 1.386 1.250 1.190 1.156 3.078 1.886 1.638 6.314 2.920 2.353 12.71 4,303 3.182 2.776 2.571 15.89 4.849 3.482 2.999 2.757 31.82 6.965 4.541 3.747 3.365 63.66 9.925 5.841 4.604 127.3 14.09 7.453 5.598 4.773 318.3 22.33 10.21 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 0.816 0.765 0.741 0.727 636.6 31.60 12.92 8.610 3 0.941 0.920 0.906 0.896 0.889 0.883 0.879 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 0.718 0.711 0.706 0.703 4.032 3.707 3.499 3.355 3.250 3.169 6.869 5.959 5.408 5.041 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 2.447 2.365 2.306 2.262 2,612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 4.317 4.029 3.833 3.690 3.581 3.497 8 9. 4.781 4.587 10 0.700 0.697 2.228 2.201 2.179 11 12 13 14 15 0.876 0.873 0.870 0.868 3.106 3.055 4.437 0.695 0.694 0.692 0.691 0.690 0.689 3.428 3.372 3.326 3.286 4.318 4.221 4.140 2.160 2.145 2.131 2.120 2.110 3.012 2.977 2.947 2.921 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 4.073 4.015 3.965 3.922 3.883 16 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.686 3.646 3.611 3.579 3.552 17 1.069 1.067 1.066 1.064 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.740 1.734 1.729 1.725 1.721 1,717 1.714 2.224 2.214 2.898 2.878 2.861 2.845 2.831 2.819 18 19 20 0.688 0.688 0.687 0.686 0.686 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.552 2.539 2.528 2.518 2.508 2,205 2.197 2.189 2.183 21 22 1.063 1.061 1.060 1.059 3.527 3.505 3.485 3.467 3.450 3.850 3.819 3.792 3.768 3.745 23 24 25 0.685 0.685 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.123 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.374 2.364 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 1.711 1.708 1.706 1.703 3.104 3.091 3.078 3.067 3.057 3.047 0.684 0.856 0.856 0.855 0.855 0.854 0.854 0.851 1.058 1.058 1.057 1.056 1.055 3.725 3.707 3.690 3.674 3.659 3.646 26 27 28 0.684 0.684 1.315 1.314 1.313 0.683 0.683 0.683 2.052 2.048 2.045 2.042 2.021 3.435 3.421 3.408 3.396 3.385 1.701 1.699 29 30 40 50 60 80 1.311 1.310 1.303 1.299 1.296 1.292 1.290 1.282 1.055 1.050 1.047 3.038 3.030 2.971 2.937 1.697 0.681 0.679 0.679 0.678 0.677 0.675 0.674 1.684 2.704 2.678 2.660 2.639 3.307 0.849 0.848 0.846 0.845 3.551 3.496 3.460 3.416 3.390 3.300 3.291 1.676 1.671 1.664 2.009 2.000 1.990 2.109 2.099 2.088 2.081 3.261 1.045 2.915 2.887 3.232 3.195 3.174 1.043 100 1.042 1.037 1.036 1.660 1.646 1.984 2.626 2.581 2,576 2.871 2.813 2.807 1000 0.842 0.841 1.962 2.056 2.054 2.330 2.326 3.098 3.091 1.282 1.645 1.960 50% 60%% 70% 80% 90% 95% 96e 98% 99% 99.5% 99.8% 99.9% Confidence level C
Transcribed Image Text:Table entry for p and C is the critical value t with probability p lying to its right and probability C lying between -t' and t'. Probability p TABLE D t distribution critical values Upper-tail probability p dí .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 0005 1.000 1.376 1.061 0.978 1.963 1.386 1.250 1.190 1.156 3.078 1.886 1.638 6.314 2.920 2.353 12.71 4,303 3.182 2.776 2.571 15.89 4.849 3.482 2.999 2.757 31.82 6.965 4.541 3.747 3.365 63.66 9.925 5.841 4.604 127.3 14.09 7.453 5.598 4.773 318.3 22.33 10.21 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 0.816 0.765 0.741 0.727 636.6 31.60 12.92 8.610 3 0.941 0.920 0.906 0.896 0.889 0.883 0.879 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 0.718 0.711 0.706 0.703 4.032 3.707 3.499 3.355 3.250 3.169 6.869 5.959 5.408 5.041 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 2.447 2.365 2.306 2.262 2,612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 4.317 4.029 3.833 3.690 3.581 3.497 8 9. 4.781 4.587 10 0.700 0.697 2.228 2.201 2.179 11 12 13 14 15 0.876 0.873 0.870 0.868 3.106 3.055 4.437 0.695 0.694 0.692 0.691 0.690 0.689 3.428 3.372 3.326 3.286 4.318 4.221 4.140 2.160 2.145 2.131 2.120 2.110 3.012 2.977 2.947 2.921 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 4.073 4.015 3.965 3.922 3.883 16 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.686 3.646 3.611 3.579 3.552 17 1.069 1.067 1.066 1.064 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.740 1.734 1.729 1.725 1.721 1,717 1.714 2.224 2.214 2.898 2.878 2.861 2.845 2.831 2.819 18 19 20 0.688 0.688 0.687 0.686 0.686 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.552 2.539 2.528 2.518 2.508 2,205 2.197 2.189 2.183 21 22 1.063 1.061 1.060 1.059 3.527 3.505 3.485 3.467 3.450 3.850 3.819 3.792 3.768 3.745 23 24 25 0.685 0.685 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.123 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.374 2.364 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 1.711 1.708 1.706 1.703 3.104 3.091 3.078 3.067 3.057 3.047 0.684 0.856 0.856 0.855 0.855 0.854 0.854 0.851 1.058 1.058 1.057 1.056 1.055 3.725 3.707 3.690 3.674 3.659 3.646 26 27 28 0.684 0.684 1.315 1.314 1.313 0.683 0.683 0.683 2.052 2.048 2.045 2.042 2.021 3.435 3.421 3.408 3.396 3.385 1.701 1.699 29 30 40 50 60 80 1.311 1.310 1.303 1.299 1.296 1.292 1.290 1.282 1.055 1.050 1.047 3.038 3.030 2.971 2.937 1.697 0.681 0.679 0.679 0.678 0.677 0.675 0.674 1.684 2.704 2.678 2.660 2.639 3.307 0.849 0.848 0.846 0.845 3.551 3.496 3.460 3.416 3.390 3.300 3.291 1.676 1.671 1.664 2.009 2.000 1.990 2.109 2.099 2.088 2.081 3.261 1.045 2.915 2.887 3.232 3.195 3.174 1.043 100 1.042 1.037 1.036 1.660 1.646 1.984 2.626 2.581 2,576 2.871 2.813 2.807 1000 0.842 0.841 1.962 2.056 2.054 2.330 2.326 3.098 3.091 1.282 1.645 1.960 50% 60%% 70% 80% 90% 95% 96e 98% 99% 99.5% 99.8% 99.9% Confidence level C
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