Question

E217 how work for full credia, allp 4 decimal plakesme h theie targes ( or the confidence nera. eviesce al elaces) (a) Mordo claims that half of each casey? answers to of 400 of Doctor Strange's mystic bolts, 220 of them his to answer Ho: Hai p- value 0.1% 5% 10% 15% 20% yes no yes no yes no yes no yes no yes no yes no (b) we can be 99.9% confident that the proportion of all of Doctor Strange's between what two numbers? mystic bolts which hit their target is our sample isn't among the 1 out of 100 most extreme samples, the proportion of all of Doctor nystic bolts which hit their target is between what two numbers?

Answer 1

pcap = 220/400 = 0.5500

H0: p = 0.5

Ha: p not equals 0.5

Test statistic,

z = (0.55 - 0.5)/sqrt(0.5*0.5/400)

z = 2

p-value = 0.0455

For 5%, 10% and 20%, p-value is less than significance level, hence reject null hypothesis.

Hence in for 0.1%, 1% and 3% Mordo's claim hold true.

b)

n = 400

p = 0.55

z-value of 99.9% CI = 2.5758

SE = sqrt(p*(1-p)/n) = 0.02487

ME = z*SE = 0.06407

Lower Limit = p - ME = 0.48593

Upper Limit = p + ME = 0.61407

99.9% CI (0.4859 , 0.6141 )

c)

48.59 and 61.41