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Pet Phone Calls: Validating a 37% Claim with Z-test
Chapter , Problem 25(choose chapter or problem)
Talk to the Animals In a survey conducted by the American Animal Hospital Association, 37% of respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have the right to be skeptical? Use a 0.05 level of significance.
Questions & Answers
QUESTION:
Talk to the Animals In a survey conducted by the American Animal Hospital Association, 37% of respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have the right to be skeptical? Use a 0.05 level of significance.
ANSWER:Step 1 of 3
Given, 37% of respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the answering machine or telephone.
\(p_{0}=37 \%=0.37 \text { and } 1-p_{0}=0.63\)
Here, \(\mathrm{n}=150, \mathrm{x}=54, \alpha=0.05\)
\(\widehat{p}=\frac{x}{n}=\frac{54}{150}=0.36 .\)
Consider the null and alternative hypothesis are
\(H_{0}: p=0.37\) against
\(H_{1}: \mathrm{p}<0.37\)
\(n p_{0}\left(1-p_{0}\right)=25.5>10 .\)
\(\begin{array}{c}
150 * 0.37(1-0.37)>10 \\
34.965>10 \\
35>10
\end{array}\)
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Pet Phone Calls: Validating a 37% Claim with Z-test
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Explore a claim from the American Animal Hospital Association that 37% of pet owners communicate with their pets over the phone. Through hypothesis testing and a z-test, evaluate a skeptical veterinarian's doubts. Conclusions shed light on pet owners' unique communication habits.