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 boxplot indicates there are no outliers.

5.05	5.72	4.38	4.80
5.02	4.5	4.74	5.19
4.61	4.76	4.56	5.69

Table of Critical T-values: t-Distribution Area in Right Tail Degrees of Freedom 0.25 0.2 0.15 0.1 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.657 127.321 318.309 636.619 2 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 3 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.215 12.924 4 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 5 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 6 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 7 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 8 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 19 0.688 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 21 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 22 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 23 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 0.685 0.857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 25 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 27 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 28 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 29 0.682 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 0.682 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 31 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 32 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 33 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356 3.611 34 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 35 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 36 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 37 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.326 3.574 38 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566 39 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 2.976 3.313 3.558 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 50 0.679 0.849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 0.679 0.848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 70 0.678 0.847 1.044 1.294 1.667 1.994 2.093 2.381 2.648 2.899 3.211 3.435 80 0.678 0.846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 90 0.677 0.846 1.042 1.291 1.662 1.987 2.084 2.368 2.632 2.878 3.183 3.402 100 0.677 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1000 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 z 0.674 0.842 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.090 3.291.

(a) Determine a point estimate for the population mean. A point estimate for the population mean is enter your response here. (Round to two decimal places as needed.)

Part 2 (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.) A. There is 95% confidence that the population mean pH of rain water is between enter your response here and enter your response here. B. There is a 95% probability that the true mean pH of rain water is between enter your response here and enter your response here. C. If repeated samples are taken, 95% of them will have a sample pH of rain water between enter your response here and enter your response here.

Part 3 (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.) A. If repeated samples are taken, 99% of them will have a sample pH of rain water between enter your response here and enter your response here. B. There is a 99% probability that the true mean pH of rain water is between enter your response here and enter your response here. C. There is 99% confidence that the population mean pH of rain water is between enter your response here and enter your response here.

Part 4 (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 increases. decreases. This makes sense since the point estimate sample size margin of error increases as well. decreases as well.