In Gotham, Batman sends 28 of the 41 bad guys to he\'s arrested to Arkham Asylum

Question

In Gotham, Batman sends 28 of the 41 bad guys to he's arrested to Arkham Asylum. In Metropolis, Superman successful arrests 17 out of 37 bad guys. It is said with 99% confident that Batman has a better success rate than Superman Test the claim. Use Batman's capture percentage as p_1 and Superman's as p_2. H_0: p_1 11 P_2 versus H_1: p_1 12 p_2 The level of significance is alpha = 13 P-value = 14 P-value 15 alpha 16 reject the null hypothesis. There 17 sufficient evidence at the level of significance to support the claim.

Explanation / Answer

step1Ho: p1=p2 ; Ha : p1>p2

step 2: level of significance =0.01

step 3: p1 =28/41=0.683 ; n1=41

p2=17/37=0.459 ; n2=37

hence std error of differnce =(p1(1-p1)/n1+p2(1-p2)/n2)1/2 =0.1095

hence test stat z=(p1-p2)/std error =2.0405

for above p value =0.0207

p vlaue>alpha

step 4: we fail to reject the null

step 5: there is not sufficient

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