Rework Exercise 15 using the alternative formula and compare the results.

Use the following information. When you know the number of successes x, the sample size n, and the population proportion p, it can be easier to use the formula

z = x – np / √npq

to find the standardized test statistic when using a z-test for a population proportion p.

Exercise 15

A humane society claims that less than 35% of U.S. households own a dog. In a random sample of 400 U.S. households, 156 say they own a dog. At α = 0.10, is there enough evidence to support the society’s claim?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Find the standardized test statistic z,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim. If convenient, use technology.