You wonder if the Incredible Hulk can throw a puny human further than Thor can t

Question

You wonder if the Incredible Hulk can throw a puny human further than Thor can throw his hammer. The Incredible Hulk throws 11 puny humans an average of 77.6 feet with a variance of 2.9 feet^2, while Thor throws his hammer 21 times for an average distance of 71.9 feet and a variance of 1.9 feet^2. Assume that the throwing distances for the Incredible Hulk and Thor are normally distributed. (a) Are the variances of the throwing distances between the Incredible Hulk and Thor different? Carry out a hypothesis test at the 2% level to answer this question. (b) Carry out a test, based on your answer to part a), at the 5% significance level to determine whether, on average, the Incredible Hulk throws puny humans further than Thor throws his hammer.

Explanation / Answer

a)

H0: 12 = 22

H1: 12 22

FSTAT=S1^2/S2^2

=2.9/1.9

=1.526

FCRIT with 2.91482065 and FSTAT is 1.526 and hence, cannot reject the null hypothesis. It shows there is no difference between the variances.

b)

H0: 1 – 2 0

H1: 1 – 2 > 0

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (11-1)*2.9+(21-1)*1.9/10+20

         =2.23

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(77.6-71.9)-0/2.23(1/11+1/21)

       =5.7/0.5558

       =10.27

tCRIT is 1.697 and hence reject the null hypothesis. There is evidence to prove that Incredible Hulk throws puny humans faster than Thor.

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