Question

A humane society claims that less than

thirty two percent

of U.S. households own a dog. In a random sample of

four hundred and nine

U.S.​ households,

153

say they own a dog. At

alphaαequals=0.04

is there enough evidence to support the​ society's claim?​(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

​(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

Upper H0

and

Upper H Subscript aHa​?

(b) What is​ (are) the critical​ value(s)?

The critical​ value(s) is/are

___

use a comma if needed and round to 2 decimal places if it is necessary

show a graph with the rejection region shaded correctly?

​(c) What is the standardized test​ statistic?

z=___ round to two decimal places as needed

(d) Which of the following is the correct conclusion for the​ test?

reject H0 or fail to reject H0

(e) Interpret your results. Choose the correct answer below.

A. there is enough evidence to support the claim that thirty two percent of U.S. households own a dog.

B. There is enough evidence to support the claim that less than thirty two percent of U.S. households own a dog.

C. there is not enough evidence to support the claim that less than 32% of U.S. households own a dog.

D. there is not enough evidence to support the claim that 32% of U.S. households own a dog.

Answer 1

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 0.04 level of significance if

Now,

The critical value is

The value of the test statistic =

Since , so we fail to reject H₀ at 0.04 level of significance.

Conclusion : C. there is not enough evidence to support the claim that less than 32% of U.S. households own a dog.