Question

It is generally believed that 45% of all pet owners feel that pet food is too expensive. A survey found that out of 300 pet owners, 50% said they felt that pet food was too expensive.

a. Estimate the probability that more than 50% of all pet owners think pet food is too expensive

b, Based on your answer in (a), are you surprised that more than 50% of all pet owners think pet food is too expensive? Explain.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.4500
sample size       =n=	300
std error of proportion=σp=√(p*(1-p)/n)=	0.0287

a)

probability that more than 50% of all pet owners think pet food is too expensive::

probability =P(X>0.5)=P(Z>(0.5-0.45)/0.029)=P(Z>1.74)=1-P(Z<1.74)=1-0.9591=0.0409

b)

since above probability is less than 0.05 , it is an unusual event and one should be surprised if true population proportion is 0.45.