A humane society claims that less than 35% of U.S households own a dog. In a ran

Question

A humane society claims that less than 35% of U.S households own a dog. In a random sample of 404 U.S. households, 154 say they own a dog. At alpha = 0.10, is there enough evidence to support the society's claim? (a) Write the claim mathematically and identify H_0 and H_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. (a) Which of the following correctly states H_0 and H_a? A. H_0: p greaterthanorequalto 0.35 H_a: p

Explanation / Answer

a) option A) is correct as we want to know if less than 35 % own a dog.

b) for alpha = 0.10

critical values = -1.282

rejection region TS< -1.282

c) n = 404 ,X = 154

p^ = X/n = 154/404 = 0.381188

TS = (p^ -p)/sqrt(pq/n)

= (0.381188 - 0.35)/sqrt(0.35*0.65/404)

= 1.3142788 = 1.31

d) since TS > critical value

we fail to reject the null and conclude that there is no significant evidence to support the claim

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