For the following pairs, indicate which do not comply with our rules for setting up hypotheses, and explain why. For those that don’t comply, change Ha to make it correct.

Question

a. H0:𝜇= 15,Ha:𝜇=15

b. H0:𝑝 =0.4,Ha:𝑝 >0.6

c. H0: 𝜇 =123, Ha: 𝜇 < 123

d. H0: 𝜇 =123, Ha: 𝜇 = 125

e. H0:𝑝̂=0.1,Ha:𝑝̂=0.1

Answer 1

a. H0:𝜇= 15,Ha:𝜇=15

alternate hypothesis must cover region not specified in null hypothesis

H0:𝜇= 15,Ha:𝜇!=15

b. H0:𝑝 =0.4,Ha:𝑝 >0.6

alternate hypothesis must cover region not specified in null hypothesis

H0:𝑝 =0.4,Ha:𝑝 >0.4

c. H0: 𝜇 =123, Ha: 𝜇 < 123

correct

d. H0: 𝜇 =123, Ha: 𝜇 = 125

alternate hypothesis must cover region not specified in null hypothesis

H0: 𝜇 =123, Ha: 𝜇 != 123

e. H0:𝑝̂=0.1,Ha:𝑝̂=0.1

hypothesis must specify population parameters, not sample parameters

alternate hypothesis must cover region not specified in null hypothesis

H0:p=0.1,Ha:p!=0.1