Worked solution P53-Easy-1. The one-proportion z interval is (0.5123, 0.6877). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.6000\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=72, failures=48. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-2. The one-proportion z interval is (0.3255, 0.5010). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4132\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=50, failures=71. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-3. The one-proportion z interval is (0.4195, 0.5969). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5082\pm 0.0887.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=62, failures=60. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-4. The one-proportion z interval is (0.4899, 0.6645). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5772\pm 0.0873.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=71, failures=52. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-5. The one-proportion z interval is (0.5021, 0.6753). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5887\pm 0.0866.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=73, failures=51. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-6. The one-proportion z interval is (0.4083, 0.5837). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4960\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=62, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-7. The one-proportion z interval is (0.4932, 0.6656). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5794\pm 0.0862.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=73, failures=53. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-8. The one-proportion z interval is (0.3934, 0.5672). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4803\pm 0.0869.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=61, failures=66. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-9. The one-proportion z interval is (0.3746, 0.5473). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4609\pm 0.0864.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=59, failures=69. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-10. The one-proportion z interval is (0.4254, 0.5979). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5116\pm 0.0863.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=66, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-11. The one-proportion z interval is (0.4841, 0.6544). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5692\pm 0.0851.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=74, failures=56. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-12. The one-proportion z interval is (0.3353, 0.5044). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4198\pm 0.0845.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=55, failures=76. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-13. The one-proportion z interval is (0.5070, 0.6748). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5909\pm 0.0839.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=78, failures=54. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-14. The one-proportion z interval is (0.3298, 0.4972). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4135\pm 0.0837.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=55, failures=78. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-15. The one-proportion z interval is (0.5140, 0.6801). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5970\pm 0.0831.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=80, failures=54. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-16. The one-proportion z interval is (0.4642, 0.6321). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5481\pm 0.0840.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=74, failures=61. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-17. The one-proportion z interval is (0.4530, 0.6206). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5368\pm 0.0838.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=73, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-18. The one-proportion z interval is (0.4641, 0.6308). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5474\pm 0.0833.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=75, failures=62. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-19. The one-proportion z interval is (0.5198, 0.6831). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.6014\pm 0.0817.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=83, failures=55. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Easy-20. The one-proportion z interval is (0.3776, 0.5433). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4604\pm 0.0829.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=64, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-1. The one-proportion z interval is (0.5123, 0.6877). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.6000\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=72, failures=48. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-2. The one-proportion z interval is (0.3577, 0.5349). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4463\pm 0.0886.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=54, failures=67. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-3. The one-proportion z interval is (0.5114, 0.6854). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5984\pm 0.0870.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=73, failures=49. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-4. The one-proportion z interval is (0.3513, 0.5267). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4390\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=54, failures=69. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-5. The one-proportion z interval is (0.3247, 0.4979). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4113\pm 0.0866.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=51, failures=73. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-6. The one-proportion z interval is (0.3530, 0.5270). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4400\pm 0.0870.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=55, failures=70. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-7. The one-proportion z interval is (0.3344, 0.5068). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4206\pm 0.0862.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=53, failures=73. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-8. The one-proportion z interval is (0.5132, 0.6837). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5984\pm 0.0853.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=76, failures=51. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-9. The one-proportion z interval is (0.4527, 0.6254). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5391\pm 0.0864.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=69, failures=59. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-10. The one-proportion z interval is (0.3867, 0.5590). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4729\pm 0.0862.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=61, failures=68. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-11. The one-proportion z interval is (0.3758, 0.5472). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4615\pm 0.0857.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=60, failures=70. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-12. The one-proportion z interval is (0.3279, 0.4965). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4122\pm 0.0843.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=54, failures=77. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-13. The one-proportion z interval is (0.4528, 0.6229). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5379\pm 0.0851.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=71, failures=61. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-14. The one-proportion z interval is (0.3963, 0.5661). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4812\pm 0.0849.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=64, failures=69. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-15. The one-proportion z interval is (0.4453, 0.6144). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5299\pm 0.0845.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=71, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-16. The one-proportion z interval is (0.3752, 0.5433). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4593\pm 0.0841.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=62, failures=73. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-17. The one-proportion z interval is (0.4904, 0.6567). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5735\pm 0.0831.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=78, failures=58. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-18. The one-proportion z interval is (0.3692, 0.5359). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4526\pm 0.0833.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=62, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-19. The one-proportion z interval is (0.3949, 0.5616). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4783\pm 0.0833.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=66, failures=72. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Tough-20. The one-proportion z interval is (0.5082, 0.6717). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5899\pm 0.0818.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=82, failures=57. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-1. The one-proportion z interval is (0.3123, 0.4877). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4000\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=48, failures=72. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-2. The one-proportion z interval is (0.3095, 0.4839). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.3967\pm 0.0872.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=48, failures=73. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-3. The one-proportion z interval is (0.3949, 0.5723). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4836\pm 0.0887.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=59, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-4. The one-proportion z interval is (0.4733, 0.6487). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5610\pm 0.0877.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=69, failures=54. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-5. The one-proportion z interval is (0.3403, 0.5145). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4274\pm 0.0871.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=53, failures=71. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-6. The one-proportion z interval is (0.3141, 0.4859). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4000\pm 0.0859.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=50, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-7. The one-proportion z interval is (0.3733, 0.5473). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4603\pm 0.0870.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=58, failures=68. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-8. The one-proportion z interval is (0.3623, 0.5353). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4488\pm 0.0865.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=57, failures=70. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-9. The one-proportion z interval is (0.4527, 0.6254). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5391\pm 0.0864.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=69, failures=59. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-10. The one-proportion z interval is (0.3335, 0.5037). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4186\pm 0.0851.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=54, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-11. The one-proportion z interval is (0.3381, 0.5080). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4231\pm 0.0849.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=55, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-12. The one-proportion z interval is (0.4182, 0.5894). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5038\pm 0.0856.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=66, failures=65. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-13. The one-proportion z interval is (0.3326, 0.5008). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4167\pm 0.0841.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=55, failures=77. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-14. The one-proportion z interval is (0.4873, 0.6555). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5714\pm 0.0841.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=76, failures=57. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-15. The one-proportion z interval is (0.4833, 0.6511). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5672\pm 0.0839.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=76, failures=58. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-16. The one-proportion z interval is (0.4642, 0.6321). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5481\pm 0.0840.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=74, failures=61. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-17. The one-proportion z interval is (0.4530, 0.6206). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.5368\pm 0.0838.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=73, failures=63. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-18. The one-proportion z interval is (0.3836, 0.5507). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4672\pm 0.0835.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=64, failures=73. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-19. The one-proportion z interval is (0.3734, 0.5396). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4565\pm 0.0831.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=63, failures=75. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.

Worked solution P53-Toughest-20. The one-proportion z interval is (0.3989, 0.5651). $$\widehat{p}\pm 1.96\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=0.4820\pm 0.0831.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: Check randomization, the 10 percent condition if sampling without replacement, and large counts: successes=67, failures=72. Error to reject: Do not say there is a 95 percent probability this fixed population proportion lies in the computed interval.