9.2

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 boxplot indicates there are no outliers. Complete 5.30 5.72 5.24 4.80 parts a) through d) below. 5.02 4.58 4.74 5.19 543 4.76 4.56 568 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.) 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 1: Table of Critical t-Values right tai f-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 15.894 31.821 63.657 127.321 318.309 636.619 0.816 1.061 2.920 4.30 6.965 9.92 31.59 0.765 0.978 1.250 4.089 2.327 1.638 2.353 3.18 4.541 5.84 7.453 10.215 12.924 0.741 0.941 1.190 1.533 2132 4.604 7173 8.610 0.727 0.920 1.156 1.476 2015 2:571 2.757 4.032 4.773 6.869 0.718 1.134 1.440 2.447 1.119 2.612 3.143 3.707 5.208 0.711 1.415 2.36 2.517 3.499 4.785 0.706 1.106 1.397 2.449 2.998 0.703 1.100 1.383 2.262 2.821 0.700 0.879 1093 1.372 2.228 2.359 2.764 0.60% 0.876 1.088 1.363 2.201 2.328 3.106 4.437 2.17 2.303 0.694 2.282 0.692 3.787 0.691 1074 1.341 2.131 2.249 2.947 3.733 4.073 0.690 1.337 2.12 2.921 3.252 1.333 2.110 2.10 2. 205 1.725 2.086 1.721 2.08 3.527 3.819 2.07 3.792 2.06 2.797 2.060 2.167 2.787 3.078 3: 450 2.056 3.435 3.707 2.052 2162 3.067 2.154 3408 1310 2.045 2150 3.038 3.659 1.697 3.030 3.385 3. 646 2.040 2.144 3.022 3.375 2.037 2.141 3.365 2.032 2.136 2441 3.008 3.002 3.348 2.030 2.133 2438 2.996 3.340 0.681 1.688 2.021 3.333 3.582 2.026 3.326 3.319 0.68 2.980 3.313 3.558 1.303 2.021 2:123 2423 2.976 2.971 3.551 0.679 1.209 2.009 2.937 3.261 0.679 1.296 2.000 2.099 2.915 3.232 3.460 0.678 1.294 3.435 0.678 1.292 1.291 2.088 2.374 2.887 3.195 3.416 0.677 0.846 1.662 2.08 2.368 2.632 2.878 3.183 3.402 0.677 0.845 1.290 2.626 2.871 3.174 3.390 0.675 0.842 2 364 1037 1.282 2.081 3.098 0.674 1036 1282 1.645 1.960 2.056 2 326 2 576 Degrees of 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 Freedom f-Distribution Area in Right Tail (1) O decreases. (2) O margin of error (3) O increases as well. increases. O point estimate O decreases as well. O sample size