Assuming a random sample from a large population for which o

Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes n is the large-sample z test appropriate:

(a)    H₀: p = 0.2, n = 25

appropriatenot appropriate    

(b)    H₀: p = 0.5, n = 225

appropriatenot appropriate    

(c)    H₀: p = 0.9, n = 100

appropriatenot appropriate    

(d)    H₀: p = 0.05, n = 65

appropriatenot appropriate

Solution

Np=0.2*25=5<10

Npq=0.2*0.8*25=4<10

Assuming a random sample from a large population the above is not appropriate to use large-sample z test.

Np=0.5*225=112.5>10

Npq=0.5*0.5*225=56.25>10

Assuming a random sample from a large population the above is appropriate to use large-sample z test.