Question

A humane society claims that less than 34​% of U.S. households own a dog. In a random sample of 399 U.S.​ households, 151 say they own a dog. At alphaequals0.04​, is there enough evidence to support the​ society's claim? ​(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic.​ (d) Decide whether to reject or fail to reject the null​ hypothesis, and​ (e) interpret the decision in the context of the original claim.

Answer 1

from above

a)

null Hypothesis:               Ho:		p	=	0.340
alternate Hypothesis:    Ha:		p	<	0.340

b)

  critical​ value( z= -1.75

rejection region z < -1.75

c)

standardized test statistic z =1.62

d)

as test statistic does not fall in rejection region, fail to reject the null​ hypothesis

e)

we can not conclude that  less than 34​% of U.S. households own a dog