Question

in a survey, 30% of the respondents stated that they talk to their pets on the telephone. a veterinarian believes it is less than that, so he randomly selected 170 pet owners and discovered that 55 of them spoke to their pet on the telephone. does the data support the veterinarian? use the $\alpha = 0.1$ level of significance.
what are the null and alternative hypotheses?
$h_0$:
$h_1$:
(type integers or decimals. do not round.)

Explanation:

Step1: Define the parameter

Let \( p \) be the proportion of pet owners who talk to their pets on the telephone.

Step2: Formulate the null hypothesis

The null hypothesis \( H_0 \) is a statement of no difference or the status quo. Here, the survey stated 30% (or 0.3) of respondents talk to their pets on the telephone. So, \( H_0: p = 0.3 \)

Step3: Formulate the alternative hypothesis

The veterinarian believes the proportion is less than 30%. So, the alternative hypothesis \( H_1 \) is \( H_1: p < 0.3 \)

Answer:

\( H_0: p = 0.3 \)
\( H_1: p < 0.3 \)