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Exploring a Single Confidence Interval for a Proportion

Exploring a Single Confidence Interval for a Proportion
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2015-01-24 21:05
Probability & StatisticsGeometric ConstructionGraphing
In collections AP Stats Exam Review Confidence Intervals
This example demonstrates how to explore a single proportion confidence interval using GeoGebra, covering graphical representation and calculation. Key math concepts include confidence intervals, normal distribution, sample proportion, and z-scores. GeoGebra commands used are InverseNormal for calculating interval endpoints, Segment for drawing the interval, If for conditional display, and Sum for potential statistical computations. Suitable for high school students and beginners in statistics learning proportion estimation and confidence intervals.

GeoGebra Commands & Parameters

  1. InverseNormal(0, 1, (1 - confidence) / 2) → a
  2. Segment((C1, E1), (D1, E1)) → F1
  3. Segment((C2, E2), (D2, E2)) → F2
  4. Segment((C3, E3), (D3, E3)) → F3
  5. Segment((C4, E4), (D4, E4)) → F4
  6. Segment((C5, E5), (D5, E5)) → F5
  7. Segment((C6, E6), (D6, E6)) → F6
  8. Segment((C7, E7), (D7, E7)) → F7
  9. Segment((C8, E8), (D8, E8)) → F8
  10. Segment((C9, E9), (D9, E9)) → F9
  11. Segment((C10, E10), (D10, E10)) → F10
  12. Segment((C11, E11), (D11, E11)) → F11
  13. Segment((C12, E12), (D12, E12)) → F12
  14. Segment((C13, E13), (D13, E13)) → F13
  15. Segment((C14, E14), (D14, E14)) → F14
  16. Segment((C15, E15), (D15, E15)) → F15
  17. Segment((C16, E16), (D16, E16)) → F16
  18. Segment((C17, E17), (D17, E17)) → F17
  19. Segment((C18, E18), (D18, E18)) → F18
  20. Segment((C19, E19), (D19, E19)) → F19
  21. Segment((C20, E20), (D20, E20)) → F20
  22. Segment((C21, E21), (D21, E21)) → F21
  23. Segment((C22, E22), (D22, E22)) → F22
  24. Segment((C23, E23), (D23, E23)) → F23
  25. Segment((C24, E24), (D24, E24)) → F24
  26. Segment((C25, E25), (D25, E25)) → F25
  27. Segment((C26, E26), (D26, E26)) → F26
  28. Segment((C27, E27), (D27, E27)) → F27
  29. Segment((C28, E28), (D28, E28)) → F28
  30. Segment((C29, E29), (D29, E29)) → F29
  31. Segment((C30, E30), (D30, E30)) → F30
  32. Segment((C31, E31), (D31, E31)) → F31
  33. Segment((C32, E32), (D32, E32)) → F32
  34. Segment((C33, E33), (D33, E33)) → F33
  35. Segment((C34, E34), (D34, E34)) → F34
  36. Segment((C35, E35), (D35, E35)) → F35
  37. Segment((C36, E36), (D36, E36)) → F36
  38. Segment((C37, E37), (D37, E37)) → F37
  39. Segment((C38, E38), (D38, E38)) → F38
  40. Segment((C39, E39), (D39, E39)) → F39
  41. Segment((C40, E40), (D40, E40)) → F40
  42. Segment((C41, E41), (D41, E41)) → F41
  43. Segment((C42, E42), (D42, E42)) → F42
  44. Segment((C43, E43), (D43, E43)) → F43
  45. Segment((C44, E44), (D44, E44)) → F44
  46. Segment((C45, E45), (D45, E45)) → F45
  47. Segment((C46, E46), (D46, E46)) → F46
  48. Segment((C47, E47), (D47, E47)) → F47
  49. Segment((C48, E48), (D48, E48)) → F48
  50. Segment((C49, E49), (D49, E49)) → F49
  51. Segment((C50, E50), (D50, E50)) → F50
  52. Segment((C51, E51), (D51, E51)) → F51
  53. Segment((C52, E52), (D52, E52)) → F52
  54. Segment((C53, E53), (D53, E53)) → F53
  55. Segment((C54, E54), (D54, E54)) → F54
  56. Segment((C55, E55), (D55, E55)) → F55
  57. Segment((C56, E56), (D56, E56)) → F56
  58. Segment((C57, E57), (D57, E57)) → F57
  59. Segment((C58, E58), (D58, E58)) → F58
  60. Segment((C59, E59), (D59, E59)) → F59
  61. Segment((C60, E60), (D60, E60)) → F60
  62. Segment((C61, E61), (D61, E61)) → F61
  63. Segment((C62, E62), (D62, E62)) → F62
  64. Segment((C63, E63), (D63, E63)) → F63
  65. Segment((C64, E64), (D64, E64)) → F64
  66. Segment((C65, E65), (D65, E65)) → F65
  67. Segment((C66, E66), (D66, E66)) → F66
  68. Segment((C67, E67), (D67, E67)) → F67
  69. Segment((C68, E68), (D68, E68)) → F68
  70. Segment((C69, E69), (D69, E69)) → F69
  71. Segment((C70, E70), (D70, E70)) → F70
  72. Segment((C71, E71), (D71, E71)) → F71
  73. Segment((C72, E72), (D72, E72)) → F72
  74. Segment((C73, E73), (D73, E73)) → F73
  75. Segment((C74, E74), (D74, E74)) → F74
  76. Segment((C75, E75), (D75, E75)) → F75
  77. Segment((C76, E76), (D76, E76)) → F76
  78. Segment((C77, E77), (D77, E77)) → F77
  79. Segment((C78, E78), (D78, E78)) → F78
  80. Segment((C79, E79), (D79, E79)) → F79
  81. Segment((C80, E80), (D80, E80)) → F80
  82. Segment((C81, E81), (D81, E81)) → F81
  83. Segment((C82, E82), (D82, E82)) → F82
  84. Segment((C83, E83), (D83, E83)) → F83
  85. Segment((C84, E84), (D84, E84)) → F84
  86. Segment((C85, E85), (D85, E85)) → F85
  87. Segment((C86, E86), (D86, E86)) → F86
  88. Segment((C87, E87), (D87, E87)) → F87
  89. Segment((C88, E88), (D88, E88)) → F88
  90. Segment((C89, E89), (D89, E89)) → F89
  91. Segment((C90, E90), (D90, E90)) → F90
  92. Segment((C91, E91), (D91, E91)) → F91
  93. Segment((C92, E92), (D92, E92)) → F92
  94. Segment((C93, E93), (D93, E93)) → F93
  95. Segment((C94, E94), (D94, E94)) → F94
  96. Segment((C95, E95), (D95, E95)) → F95
  97. Segment((C96, E96), (D96, E96)) → F96
  98. Segment((C97, E97), (D97, E97)) → F97
  99. Segment((C98, E98), (D98, E98)) → F98
  100. Segment((C99, E99), (D99, E99)) → F99
  101. Segment((C100, E100), (D100, E100)) → F100
  102. If(D1 ≤ p ≤ C1, 1, 0) → H1
  103. If(D2 ≤ p ≤ C2, 1, 0) → H2
  104. If(D3 ≤ p ≤ C3, 1, 0) → H3
  105. If(D4 ≤ p ≤ C4, 1, 0) → H4
  106. If(D5 ≤ p ≤ C5, 1, 0) → H5
  107. If(D6 ≤ p ≤ C6, 1, 0) → H6
  108. If(D7 ≤ p ≤ C7, 1, 0) → H7
  109. If(D8 ≤ p ≤ C8, 1, 0) → H8
  110. If(D9 ≤ p ≤ C9, 1, 0) → H9
  111. If(D10 ≤ p ≤ C10, 1, 0) → H10
  112. If(D11 ≤ p ≤ C11, 1, 0) → H11
  113. If(D12 ≤ p ≤ C12, 1, 0) → H12
  114. If(D13 ≤ p ≤ C13, 1, 0) → H13
  115. If(D14 ≤ p ≤ C14, 1, 0) → H14
  116. If(D15 ≤ p ≤ C15, 1, 0) → H15
  117. If(D16 ≤ p ≤ C16, 1, 0) → H16
  118. If(D17 ≤ p ≤ C17, 1, 0) → H17
  119. If(D18 ≤ p ≤ C18, 1, 0) → H18
  120. If(D19 ≤ p ≤ C19, 1, 0) → H19
  121. If(D20 ≤ p ≤ C20, 1, 0) → H20
  122. If(D21 ≤ p ≤ C21, 1, 0) → H21
  123. If(D22 ≤ p ≤ C22, 1, 0) → H22
  124. If(D23 ≤ p ≤ C23, 1, 0) → H23
  125. If(D24 ≤ p ≤ C24, 1, 0) → H24
  126. If(D25 ≤ p ≤ C25, 1, 0) → H25
  127. If(D26 ≤ p ≤ C26, 1, 0) → H26
  128. If(D27 ≤ p ≤ C27, 1, 0) → H27
  129. If(D28 ≤ p ≤ C28, 1, 0) → H28
  130. If(D29 ≤ p ≤ C29, 1, 0) → H29
  131. If(D30 ≤ p ≤ C30, 1, 0) → H30
  132. If(D31 ≤ p ≤ C31, 1, 0) → H31
  133. If(D32 ≤ p ≤ C32, 1, 0) → H32
  134. If(D33 ≤ p ≤ C33, 1, 0) → H33
  135. If(D34 ≤ p ≤ C34, 1, 0) → H34
  136. If(D35 ≤ p ≤ C35, 1, 0) → H35
  137. If(D36 ≤ p ≤ C36, 1, 0) → H36
  138. If(D37 ≤ p ≤ C37, 1, 0) → H37
  139. If(D38 ≤ p ≤ C38, 1, 0) → H38
  140. If(D39 ≤ p ≤ C39, 1, 0) → H39
  141. If(D40 ≤ p ≤ C40, 1, 0) → H40
  142. If(D41 ≤ p ≤ C41, 1, 0) → H41
  143. If(D42 ≤ p ≤ C42, 1, 0) → H42
  144. If(D43 ≤ p ≤ C43, 1, 0) → H43
  145. If(D44 ≤ p ≤ C44, 1, 0) → H44
  146. If(D45 ≤ p ≤ C45, 1, 0) → H45
  147. If(D46 ≤ p ≤ C46, 1, 0) → H46
  148. If(D47 ≤ p ≤ C47, 1, 0) → H47
  149. If(D48 ≤ p ≤ C48, 1, 0) → H48
  150. If(D49 ≤ p ≤ C49, 1, 0) → H49
  151. If(D50 ≤ p ≤ C50, 1, 0) → H50
  152. If(D51 ≤ p ≤ C51, 1, 0) → H51
  153. If(D52 ≤ p ≤ C52, 1, 0) → H52
  154. If(D53 ≤ p ≤ C53, 1, 0) → H53
  155. If(D54 ≤ p ≤ C54, 1, 0) → H54
  156. If(D55 ≤ p ≤ C55, 1, 0) → H55
  157. If(D56 ≤ p ≤ C56, 1, 0) → H56
  158. If(D57 ≤ p ≤ C57, 1, 0) → H57
  159. If(D58 ≤ p ≤ C58, 1, 0) → H58
  160. If(D59 ≤ p ≤ C59, 1, 0) → H59
  161. If(D60 ≤ p ≤ C60, 1, 0) → H60
  162. If(D61 ≤ p ≤ C61, 1, 0) → H61
  163. If(D62 ≤ p ≤ C62, 1, 0) → H62
  164. If(D63 ≤ p ≤ C63, 1, 0) → H63
  165. If(D64 ≤ p ≤ C64, 1, 0) → H64
  166. If(D65 ≤ p ≤ C65, 1, 0) → H65
  167. If(D66 ≤ p ≤ C66, 1, 0) → H66
  168. If(D67 ≤ p ≤ C67, 1, 0) → H67
  169. If(D68 ≤ p ≤ C68, 1, 0) → H68
  170. If(D69 ≤ p ≤ C69, 1, 0) → H69
  171. If(D70 ≤ p ≤ C70, 1, 0) → H70
  172. If(D71 ≤ p ≤ C71, 1, 0) → H71
  173. If(D72 ≤ p ≤ C72, 1, 0) → H72
  174. If(D73 ≤ p ≤ C73, 1, 0) → H73
  175. If(D74 ≤ p ≤ C74, 1, 0) → H74
  176. If(D75 ≤ p ≤ C75, 1, 0) → H75
  177. If(D76 ≤ p ≤ C76, 1, 0) → H76
  178. If(D77 ≤ p ≤ C77, 1, 0) → H77
  179. If(D78 ≤ p ≤ C78, 1, 0) → H78
  180. If(D79 ≤ p ≤ C79, 1, 0) → H79
  181. If(D80 ≤ p ≤ C80, 1, 0) → H80
  182. If(D81 ≤ p ≤ C81, 1, 0) → H81
  183. If(D82 ≤ p ≤ C82, 1, 0) → H82
  184. If(D83 ≤ p ≤ C83, 1, 0) → H83
  185. If(D84 ≤ p ≤ C84, 1, 0) → H84
  186. If(D85 ≤ p ≤ C85, 1, 0) → H85
  187. If(D86 ≤ p ≤ C86, 1, 0) → H86
  188. If(D87 ≤ p ≤ C87, 1, 0) → H87
  189. If(D88 ≤ p ≤ C88, 1, 0) → H88
  190. If(D89 ≤ p ≤ C89, 1, 0) → H89
  191. If(D90 ≤ p ≤ C90, 1, 0) → H90
  192. If(D91 ≤ p ≤ C91, 1, 0) → H91
  193. If(D92 ≤ p ≤ C92, 1, 0) → H92
  194. If(D93 ≤ p ≤ C93, 1, 0) → H93
  195. If(D94 ≤ p ≤ C94, 1, 0) → H94
  196. If(D95 ≤ p ≤ C95, 1, 0) → H95
  197. If(D96 ≤ p ≤ C96, 1, 0) → H96
  198. If(D97 ≤ p ≤ C97, 1, 0) → H97
  199. If(D98 ≤ p ≤ C98, 1, 0) → H98
  200. If(D99 ≤ p ≤ C99, 1, 0) → H99
  201. If(D100 ≤ p ≤ C100, 1, 0) → H100
  202. Sum(H1:H100) → b

AI Drawing Prompt Reference

Create a statistical plot for exploring a single proportion confidence interval. Start by computing the critical z-value from the standard normal distribution based on the confidence level, then use it to define the endpoints of each interval. Draw multiple horizontal segments, each representing a confidence interval from a different sample, stacked vertically in parallel. Mark the sample proportion on each segment and highlight any intervals that fail to contain the true population proportion. Arrange the intervals neatly to visualize how coverage varies across samples, making it easy to compare the intervals' positions and lengths.
The prompt above was compiled from the original drawing commands and is for reference only.