Homework 9.2

Print 10. The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A 5.30 5.72 5.2 4.80 boxplot indicates there are no outliers. Complete parts a) through d) below. 5.02 4.58 4.74 5.19 5.43 4.76 4.56 5.68 Click the icon to view the table of critical t-values. (a) Determine a point estimate for the population mean. A point estimate for the population mean is (Round to two decimal places as needed.) (b) Construct and interpret a 95% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to two decimal places as needed.) O A. There is a 95% probability that the true mean pH of rain water is between and O B. If repeated samples are taken, 95% of them will have a sample pH of rain water between and O C. There is 95% confidence that the population mean ph of rain water is between and (c) Construct and interpret a 99% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to two decimal places as needed.) O A. If repeated samples are taken, 99% of them will have a sample pH of rain water between and O B. There is a 99% probability that the true mean ph of rain water is between and O C. There is 99% confidence that the population mean pH of rain water is between and 'd) What happens to the interval as the level of confidence is changed? Explain why this is a logical result. As the level of confidence increases, the width of the interval (1) This makes sense since the (2) (3) 5: Table of Critical t-Values - Area in right tail 1-Distribution Degrees of Area in Right Tail Freedom 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.000 1.376 1.963 3.078 6.314 12.706 15.89 31.821 63.657 127.321 318.309 636.619 0.816 1.061 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 0.765 0.978 1.250 1.638 2.353 3.18 3.48 4.541 5.84 7.453 10.215 12 924 0.741 0.941 1.190 1.533 2132 2.776 2 009 3.747 5.598 Z173 8.610 0.727 0.920 1.156 1.476 2015 2.571 2.75' 3.365 4.032 4.773 5.893 6.869 0.718 0.906 1.134 1440 1.943 2.447 2.612 3.143 3,707 4.317 5.208 5.959 0.711 0.896 1.110 1.415 1.895 2.365 2.517 2.998 3.40 4.029 4.785 5.408 0.706 0.889 1.106 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 0.703 0.883 1.100 1.833 2.262 2.398 3.25 3.690 4.781 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 0.697 0.876 1.088 1.363 1.796 2.20 2.328 2.718 3.106 3.407 4.025 4.437 0.695 0.873 1.356 2.179 2.303 3.055 3.428 3.930 4.318 0.69 0.870 1079 1.350 1.771 2.160 2.282 2.650 3.01 3.372 3.852 4.221 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 0.691 0.866 1.074 2.131 2.249 2.947 3.286 3.733 4.073 0.690 0.865 1.337 2.120 2.235 2.583 2.921 3.252 3.686 4.015 0.689 0.863 1.069 1.333 2.110 2.224 2567 2.898 3.222 3.646 3.965 0.688 0.862 1.067 1.330 1,734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 0.68 0.861 2.093 2.205 2.861 3.174 3.579 3.883 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 0.686 0.850 1.063 1323 1.721 2.080 2.180 2.518 2.831 3.135 3.527 3.819 0.68 0.858 1.061 1.321 2.074 2.183 2.508 2.819 3.119 3.505 3.792 0.685 0.858 1.060 319 1.714 2.06 2.177 2.807 3.10 3.768 0.685 0.857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 0.684 0.856 1.058 .316 1,708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 0.684 0.856 1.058 1315 1.700 2.056 2.16 2.479 2.779 3.067 3.435 3.707 0.684 0.855 1.057 1.314 1.703 2.052 2.15 2.473 2.771 3.05 3.421 3.690 0.683 0.855 1.056 1.313 1.701 2048 2.15 2.467 2.763 3.047 3.408 3.674 0.683 0.854 1.055 1.311 2.045 2.15 2462 2.756 3.03 3.659 0.683 0.854 1.055 1.310 1.697 2.04 2.14 2.457 2.750 3.030 3.385 3.646 0.68 0.853 1.054 1.309 1.696 2 04 2.14 2.453 2.744 3.02 3.375 3.633 0.682 0.853 1054 1.309 1.604 2.037 2.141 2.449 2.738 3.015 3.365 3.622 0.68 0.853 1.053 1.308 1.692 2.03 2.13 2.445 2.733 3.00 3.611 0.68 0.852 1.052 1307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 0.682 0.852 1.052 1306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 0.68 0851 1.051 1.30 1.687 2.026 2.129 2.431 2.715 2.98 3.326 3.574 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566 0.681 0.851 1.050 1304 2.023 2.125 2 426 2.708 2.976 3.313 3.558 0.681 0.851 1.050 1303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.679 0.849 1.047 1.209 1.676 2.009 2.10 2.403 2.678 2.937 3.261 3.496 0.679 0.848 1045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 0.678 0.847 1294 1.667 1904 2.093 2.648 2.899 3.211 3.435 0.678 0.846 1043 1292 1.664 1.900 2.088 2.374 2.630 2.887 3.195 3.416 0.677 0.846 1.042 1.291 1.662 1.987 2.084 2.368 2.632 2.878 3.183 3.402 0.67 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1090 0.675 0.842 1.037 1.282 1.646 1962 2.05 2.330 2.58 2.813 3.098 3.300 0.674 0.842 1.036 1282 1.645 1.960 2.054 2.326 2.576 2.807 3.090 3.291 Degrees of 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.005 0.0025 0.001 0.0005 Freedom f-Distribution Area in Right Tail (1) O decreases. (2) O margin of error O increases as well. O increases. O point estimate decreases as well. O sample size 11. The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts (a) through (c) below. 68.28 79.08 83.92 80.68 86.25 101.83 99.12 Click the icon to view the table of critical t-values. (a) Determine a point estimate for the population mean travel tax. A point estimate for the population mean travel tax is $ (Round to two decimal places as needed.) (b) Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip. Select the correct choice below and fill in the answer boxes to complete your choice. Round to two decimal places as needed.) O A. The travel tax is between $ and $ for % of all cities. O B. One can be % confident that the mean travel tax for all cities is between $ and $ O C. One can be % confident that the all cities have a travel tax between $ and $