Question

2) A humane society claims that 30% of U.S. households own a cat. In a random sample of 210 U.S. households, 80 say they own a cat. Is there enough evidence to show this percent has changed? Use a level of significance of 0.05.

Answer 1

There is enough evidence to reject the humane society claims

Explanation:

Given:

p = 0.3

q = 1 - p = 1 - 0.3 = 0.7

n = 210

x = 80

Therefore:

`\hat{p}=(x)/(n)=(80)/(210)=0.381`

The critical values are:

`Z_0=\pm1.96\text{ due }\alpha=0.05`

The test statistic is:

`\begin{gathered} Z=\frac{\hat{p}-p}{\sqrt[]{(pq)/(n)}} \\ \text{ replacing:} \\ Z=\frac{0.381-0.3}{\sqrt{(0.3\cdot0.7)/(210)}} \\ Z=2.56 \end{gathered}`

Observe that

Z < 1.96

Therefore, reject the null hypothesis

There is enough evidence to reject the humane society claims