MathJaxMap['math_1'] = 'online course→observe GMAT scores';
MathJaxMap['math_2'] = 'treatment→observe response';
MathJaxMap['math_3'] = '{26, 29, 46, 4, 25, 1 1, 12, 14, 41, 7, 3, 17, 22, 2, 15, 42, 39, 8, 43, 47, 21, 37, 9, 24, 20}';
MathJaxMap['math_4'] = 'p̂=8551484=0.59636or approximately60%';
MathJaxMap['math_5'] = 'Sample 1:p̂=55100=0.55Sample 2:p̂=62100=0.62⋮⋮⋮Sample 1000: p̂=63100=0.63';
MathJaxMap['math_6'] = 'p̂=count of successes in the samplen';
MathJaxMap['math_7'] = 'p(1−p)n';
MathJaxMap['math_8'] = 'p(1−p)n=(0.6)(0.4)1500≈0.0126';
MathJaxMap['math_9'] = 'p̂±2p(1−p)n';
MathJaxMap['math_10'] = 'p̂±2p̂(1−p̂)n';
MathJaxMap['math_11'] = 'p̂=4621005≈0.4597';
MathJaxMap['math_12'] = 'p̂±2p̂(1−p̂)n=0.4597±2(0.4597)(0.5403)1005=0.4597±0.0314or45.97%±3.14%=0.4283 to 0.4911or42.83% to 49.11%';
MathJaxMap['math_13'] = 'p(1−p)n=0.14(1−0.14)500=0.14(0.86)500≈0.0155';
MathJaxMap['math_14'] = 'n';
MathJaxMap['math_15'] = 'n';
MathJaxMap['math_16'] = 'n';
MathJaxMap['math_17'] = '(≤144)';
MathJaxMap['math_18'] = 'MATH→PRB';
MathJaxMap['math_19'] = '5';
MathJaxMap['math_20'] = '1 , 27 )';
MathJaxMap['math_21'] = 'ENTER';
MathJaxMap['math_22'] = 'Math→PRB';
MathJaxMap['math_23'] = '8';
MathJaxMap['math_24'] = '1 , 27 )';
MathJaxMap['math_25'] = 'Enter =RAND()';
MathJaxMap['math_26'] = '16582879≈0.58';
MathJaxMap['math_27'] = 'p̂';
MathJaxMap['math_28'] = 'ŷ';
MathJaxMap['math_29'] = 'p̂=0.596';
MathJaxMap['math_30'] = 'p';
MathJaxMap['math_31'] = 'p';
MathJaxMap['math_32'] = 'p̂';
MathJaxMap['math_33'] = 'p̂=0.596';
MathJaxMap['math_34'] = 'p';
MathJaxMap['math_35'] = 'p̂';
MathJaxMap['math_36'] = 'p=0.6';
MathJaxMap['math_37'] = 'p̂';
MathJaxMap['math_38'] = 'p̂';
MathJaxMap['math_39'] = 'p̂';
MathJaxMap['math_40'] = 'p=0.6';
MathJaxMap['math_41'] = 'p=0.60';
MathJaxMap['math_42'] = 'p̂';
MathJaxMap['math_43'] = 'p̂';
MathJaxMap['math_44'] = 'p̂-values';
MathJaxMap['math_45'] = 'p=0.60';
MathJaxMap['math_46'] = 'p̂';
MathJaxMap['math_47'] = 'p̂';
MathJaxMap['math_48'] = 'p=0.60';
MathJaxMap['math_49'] = '(p=0.6)';
MathJaxMap['math_50'] = 'p̂';
MathJaxMap['math_51'] = 'p=0.6';
MathJaxMap['math_52'] = 'p̂';
MathJaxMap['math_53'] = 'n';
MathJaxMap['math_54'] = 'p';
MathJaxMap['math_55'] = 'p̂';
MathJaxMap['math_56'] = '(n≥30)';
MathJaxMap['math_57'] = 'p̂';
MathJaxMap['math_58'] = 'p̂';
MathJaxMap['math_59'] = 'p';
MathJaxMap['math_60'] = 'p̂';
MathJaxMap['math_61'] = 'n';
MathJaxMap['math_62'] = 'p';
MathJaxMap['math_63'] = 'p̂';
MathJaxMap['math_64'] = 'p=0.6';
MathJaxMap['math_65'] = 'p̂';
MathJaxMap['math_66'] = 'p̂';
MathJaxMap['math_67'] = 'p̂';
MathJaxMap['math_68'] = 'x̄=0.59982';
MathJaxMap['math_69'] = 's=0.01255';
MathJaxMap['math_70'] = 'p̂';
MathJaxMap['math_71'] = 'p̂';
MathJaxMap['math_72'] = 'p(1−p)/n=(0.6)(0.4)/1500=0.00016';
MathJaxMap['math_73'] = 'p̂';
MathJaxMap['math_74'] = 'p';
MathJaxMap['math_75'] = 'p̂';
MathJaxMap['math_76'] = 'p̂';
MathJaxMap['math_77'] = 'p=0.6';
MathJaxMap['math_78'] = 'p̂';
MathJaxMap['math_79'] = 'p=0.6';
MathJaxMap['math_80'] = 'p̂';
MathJaxMap['math_81'] = 'p̂';
MathJaxMap['math_82'] = 'p̂';
MathJaxMap['math_83'] = '2×0.0126';
MathJaxMap['math_84'] = 'p̂';
MathJaxMap['math_85'] = 'p̂';
MathJaxMap['math_86'] = 'p=0.6';
MathJaxMap['math_87'] = 'p';
MathJaxMap['math_88'] = 'n';
MathJaxMap['math_89'] = 'p̂';
MathJaxMap['math_90'] = 'p';
MathJaxMap['math_91'] = 'p̂';
MathJaxMap['math_92'] = 'p';
MathJaxMap['math_93'] = 'p̂−2';
MathJaxMap['math_94'] = 'p̂+2';
MathJaxMap['math_95'] = 'p';
MathJaxMap['math_96'] = 'p̂';
MathJaxMap['math_97'] = 'p';
MathJaxMap['math_98'] = 'p';
MathJaxMap['math_99'] = 'p̂';
MathJaxMap['math_100'] = 'p';
MathJaxMap['math_101'] = 'p̂';
MathJaxMap['math_102'] = 'p';
MathJaxMap['math_103'] = 'p̂';
MathJaxMap['math_104'] = 'p';
MathJaxMap['math_105'] = 'p';
MathJaxMap['math_106'] = 'p̂';
MathJaxMap['math_107'] = 'p';
MathJaxMap['math_108'] = 'p';
MathJaxMap['math_109'] = 'p';
MathJaxMap['math_110'] = 'n=1500';
MathJaxMap['math_111'] = 'p=0.7';
MathJaxMap['math_112'] = 'p';
MathJaxMap['math_113'] = 'p';
MathJaxMap['math_114'] = 'p(1−p)n';
MathJaxMap['math_115'] = 'p';
MathJaxMap['math_116'] = 'p̂';
MathJaxMap['math_117'] = 'p';
MathJaxMap['math_118'] = 'p̂';
MathJaxMap['math_119'] = 'p';
MathJaxMap['math_120'] = 'p';
MathJaxMap['math_121'] = 'n';
MathJaxMap['math_122'] = 'p';
MathJaxMap['math_123'] = 'p';
MathJaxMap['math_124'] = '0.5±0.2';
MathJaxMap['math_125'] = '0.5−0.2=0.3';
MathJaxMap['math_126'] = '0.5+0.2=0.7';
MathJaxMap['math_127'] = 'n';
MathJaxMap['math_128'] = '(≥30)';
MathJaxMap['math_129'] = 'p̂';
MathJaxMap['math_130'] = '2p̂(1−p̂)/n';
MathJaxMap['math_131'] = 'p';
MathJaxMap['math_132'] = 'p';
MathJaxMap['math_133'] = 'p';
MathJaxMap['math_134'] = 'p';
MathJaxMap['math_135'] = 'n';
MathJaxMap['math_136'] = 'n';
MathJaxMap['math_137'] = 'error=p̂(1−p̂)n=p̂(1−p̂)n';
MathJaxMap['math_138'] = 'p̂';
MathJaxMap['math_139'] = 'p';
MathJaxMap['math_140'] = 'p̂';
MathJaxMap['math_141'] = 'p=0.6';
MathJaxMap['math_142'] = 'p̂=0';
MathJaxMap['math_143'] = '(0.7)(0.3)/1500≈0.0118';
MathJaxMap['math_144'] = 'p̂=6231005≈0.6199p̂±2p̂(1−p̂)n=0.6199±2(0.6199)(0.3801)1005=0.6199±0.0306 or 61.99±3.06%=0.5893 to 0.6505 or 58.93% to 65.05%';
MathJaxMap['math_145'] = 'p̂';
MathJaxMap['math_146'] = '1498';
MathJaxMap['math_147'] = '100/4=25';
MathJaxMap['math_148'] = '2005=40';
MathJaxMap['math_149'] = '4031334≈0.30';
MathJaxMap['math_150'] = '3450=0.68, or 68%';
MathJaxMap['math_151'] = 'p=0.24';
MathJaxMap['math_152'] = 'p̂';
MathJaxMap['math_153'] = 'p̂';
MathJaxMap['math_154'] = 'p̂';
MathJaxMap['math_155'] = 'p=0.14';
MathJaxMap['math_156'] = '0.14±(2)(0.0155)=0.14±0.0310.14−0.031=0.109¯ to 0.14+0.031=0.171¯';
MathJaxMap['math_157'] = 'p̂';
MathJaxMap['math_158'] = 'p=0.24';
MathJaxMap['math_159'] = 'n=534';
MathJaxMap['math_160'] = 'p̂';
MathJaxMap['math_161'] = 'p=0.24';
MathJaxMap['math_162'] = 'n=400';
MathJaxMap['math_163'] = 'n=1600';
MathJaxMap['math_164'] = 'n=6400';
MathJaxMap['math_165'] = 'p̂';
MathJaxMap['math_166'] = '2940=0.725=72.5%';
MathJaxMap['math_167'] = '2440=0.60=60%';
MathJaxMap['math_168'] = 'p̂';
MathJaxMap['math_169'] = 'p̂';
MathJaxMap['math_170'] = 'p̂=7501785≈0.420';
MathJaxMap['math_171'] = 'p̂±2p̂(1−p̂)n=0.420±20.420(1−0.420)1785=0.420±20.420(0.580)1785≈0.420±0.0230.420−0.023=0.397 to 0.420+0.023=0.443';
MathJaxMap['math_172'] = 'p̂=171880≈0.194';
MathJaxMap['math_173'] = 'p̂±2p̂(1−p̂)n=0.194±20.194(1−0.194)880=0.194±20.194(0.806)880≈0.194±0.0270.194−0.027=0.167 to 0.194+0.027=0.221';
MathJaxMap['math_174'] = '2p̂(1−p̂)n';
MathJaxMap['math_175'] = 'n';
MathJaxMap['math_176'] = 'p̂';
MathJaxMap['math_177'] = 'p̂=0.5';
MathJaxMap['math_178'] = '2p̂(1−p̂)n=20.5(1−0.5)n=20.5(0.5)n=2(0.5)1n=1n=1n';
MathJaxMap['math_179'] = '146813,000≈0.113=11.3%';
MathJaxMap['math_180'] = 'p̂=797≈0.072';
MathJaxMap['math_181'] = 'p̂±2p̂(1−p̂)n=0.072±20.072(1−0.072)97=0.072±20.072(0.928)97≈0.072±0.0520.072−0.052=0.020 to 0.072+0.052=0.124';
MathJaxMap['math_182'] = 'p̂';
MathJaxMap['math_183'] = 'p=0.1';
MathJaxMap['math_184'] = 'p(1−p)n=0.1(1−0.1)97=0.1(0.9)97≈0.030';
MathJaxMap['math_185'] = 'p=0. 1';
MathJaxMap['math_186'] = '0.63±2(0.63)(1−0.63)1000≈0.63±0.0305';
MathJaxMap['math_187'] = '2(0.5)(0.5)1000≈0.0316; 3.1%';
MathJaxMap['math_188'] = '2(0.8)(0.2)1000≈0.0253';
MathJaxMap['math_189'] = '2(0.5)(0.5)n=0.03';
MathJaxMap['math_190'] = 'n';
MathJaxMap['math_191'] = 'n=(0.50.015)2≈1111.11';