Question

A recent survey stated that 37% of pet owners talk to their pets on the telephone. A veterinarian believes that the proportion should be lower than the survey's claim. In a random sample of 180 pet owners, 33.9% of them said they spoke to their pets on the telephone. Find the following while performing a hypothesis test to see if there is sufficient evidence that the proportion of pet owners that talk to their pets on the telephone is lower than the survey's claim. Use a significance level of α = 0.05.

a) State the null and alternative hypotheses.

b) z-test statistic. Round the standard deviation to 5 decimal places and the answer to 3 decimal places.

c) p-value

d) State if we would Fail to reject or Reject the null hypothesis.

Answer 1

a)

null Hypothesis:               Ho:   p		>=	0.370
alternate Hypothesis:    Ha: p		<	0.370

b)

sample size          n    =		180
std error   se =√(p*(1-p)/n) =		0.03599
sample proportion p̂ = x/n=		0.3390
test stat z =(p̂-p)/√(p(1-p)/n)=		-0.861

c)

from excel: p value =normsdist(-0.861) =0.1946

d)

since p value >0.05 ;  Fail to reject