Worked solution P57-Easy-1. The interval is (-0.0033, 0.2430) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1199\pm 0.1232.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-2. The interval is (0.0037, 0.2488) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1262\pm 0.1226.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-3. The interval is (0.0048, 0.2488) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1268\pm 0.1220.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-4. The interval is (-0.0062, 0.2372) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1155\pm 0.1217.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-5. The interval is (-0.0078, 0.2341) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1131\pm 0.1210.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-6. The interval is (-0.0004, 0.2404) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1200\pm 0.1204.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-7. The interval is (0.0021, 0.2426) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1223\pm 0.1203.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-8. The interval is (0.0054, 0.2434) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1244\pm 0.1190.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-9. The interval is (0.0017, 0.2404) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1210\pm 0.1193.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-10. The interval is (0.0015, 0.2393) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1204\pm 0.1189.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-11. The interval is (-0.0014, 0.2355) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1170\pm 0.1185.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-12. The interval is (0.0035, 0.2382) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1208\pm 0.1173.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-13. The interval is (0.0029, 0.2366) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1197\pm 0.1168.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-14. The interval is (-0.0014, 0.2331) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1158\pm 0.1173.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Easy-15. The interval is (-0.0010, 0.2326) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1158\pm 0.1168.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-1. The interval is (-0.0062, 0.2395) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1167\pm 0.1228.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-2. The interval is (-0.0077, 0.2361) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1142\pm 0.1219.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-3. The interval is (-0.0049, 0.2396) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1174\pm 0.1222.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-4. The interval is (-0.0004, 0.2416) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1206\pm 0.1210.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-5. The interval is (0.0008, 0.2428) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1218\pm 0.1210.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-6. The interval is (0.0049, 0.2458) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1253\pm 0.1204.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-7. The interval is (-0.0041, 0.2364) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1161\pm 0.1202.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-8. The interval is (0.0032, 0.2425) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1228\pm 0.1197.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-9. The interval is (-0.0006, 0.2381) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1188\pm 0.1193.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-10. The interval is (0.0022, 0.2398) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1210\pm 0.1188.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-11. The interval is (0.0054, 0.2419) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1236\pm 0.1183.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-12. The interval is (0.0035, 0.2382) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1208\pm 0.1173.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-13. The interval is (0.0029, 0.2366) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1197\pm 0.1168.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-14. The interval is (0.0023, 0.2350) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1186\pm 0.1163.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Tough-15. The interval is (0.0071, 0.2404) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1238\pm 0.1166.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-1. The interval is (-0.0045, 0.2417) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1186\pm 0.1231.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-2. The interval is (0.0037, 0.2488) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1262\pm 0.1226.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-3. The interval is (-0.0042, 0.2402) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1180\pm 0.1222.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-4. The interval is (0.0001, 0.2424) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1212\pm 0.1212.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-5. The interval is (0.0037, 0.2459) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1248\pm 0.1211.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-6. The interval is (-0.0004, 0.2404) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1200\pm 0.1204.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-7. The interval is (-0.0034, 0.2368) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1167\pm 0.1201.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-8. The interval is (-0.0008, 0.2384) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1188\pm 0.1196.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-9. The interval is (-0.0011, 0.2375) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1182\pm 0.1193.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-10. The interval is (-0.0033, 0.2330) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1148\pm 0.1182.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-11. The interval is (-0.0032, 0.2329) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1148\pm 0.1180.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-12. The interval is (0.0035, 0.2382) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1208\pm 0.1173.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-13. The interval is (0.0064, 0.2416) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1240\pm 0.1176.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-14. The interval is (0.0068, 0.2410) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1239\pm 0.1171.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.

Worked solution P57-Toughest-15. The interval is (0.0055, 0.2390) for group 1 minus group 2. $$({\widehat{p}}_1-{\widehat{p}}_2)\pm 1.96\sqrt{\frac{{\widehat{p}}_1(1-{\widehat{p}}_1)}{n_1}+\frac{{\widehat{p}}_2(1-{\widehat{p}}_2)}{n_2}}=0.1222\pm 0.1167.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Require independent random groups or randomized treatments, independence within groups, and at least 10 successes and 10 failures in each group. Error to reject: Do not pool the sample proportions for a confidence interval; the interval estimates an unrestricted difference.