Question

A nationwide survey claimed that at least 65​% of parents with young children condone spanking their child as a regular form of punishment. In a random sample of 100 parents with young​ children, how many would need to say that they condone spanking as a form of punishment in order to refute the claim at alpha equals 0.05?

A. You would need exactly 57 parents to support spanking to refute the claim.

B. You would need 58 or fewer parents to support spanking to refute the claim.

C. You would need more than 57 parents to support spanking to refute the claim.

D. You would need 57 or fewer parents to support spanking to refute the claim.

Answer 1

solution:

option A is right answer

i.e; You would need exactly 57 parents to support spanking to refute the claim

explaination:

given p=0.65 and n=100

hence standard error =(p*(1-p)/n)^1/2 =(0.65*(1-0.65)/100)^1/2 =0.0477

for 0.05 level and left tailed test ; critical z =-1.645

hence rejection area: phat <p+z*std error

phat<0.65-1.645*0.0477 =0.5715

therefore to refute the claim; maximum number that need to say that they condone spanking =nphat=100*0.5715

~ 57