Question

A humane society claims that less than 35% of U.S. households own a dog. In a random sample of 401 U.S.​ households,152

say they own a dog. A a=0.03​, is there enough evidence to support the​ society's claim?

​(a) Write the claim mathematically and identify Upper H0 and Upper HaHa.

​(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

a)

H0: p = 0.35

Ha: p < 0.35

b)

Critical value at 0.03 level = -1.881

c)

Sample proportion = 152 / 401 = 0.379

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.379 - 0.35 / sqrt( 0.35 * 0.65 / 401)

= 1.22

d)

Since test statistics > -1.881, do not reject H0.

e)

We conclude at 0.03 level that we fail to support the claim that less than 35% of U.S. households

own a dog.