**Title:** Testing a Veterinarian's Claim on Cat Ownership Proportion**Problem Statement:**The proportion of people that own cats is 80%. A veterinarian believes that this proportion is smaller than 80% and surveys 200 people. Test the veterinarian's claim at the significance level of α = 0.005.**Preliminary Steps:**a. **Sample Safety Verification:**Is it safe to assume that \( n \leq 0.05 \) of all subjects in the population?- Options: - Yes - Nob. **Sample Size Validation:**Verify \( np(1 - p) \geq 10 \). Round your answer to one decimal place.\[ np(1 - p) = \underline{\hspace{3cm}} \]**Testing the Claim:**a. **Null and Alternative Hypotheses:**Select the correct set of hypotheses:- \( H_0: p \leq 0.8 \) and \( H_a: p > 0.8 \)- \( H_0: \mu \leq 0.8 \) and \( H_a: \mu > 0.8 \)- \( H_0: \mu = 0.8 \) and \( H_a: \mu \neq 0.8 \)- \( H_0: p = 0.8 \) and \( H_a: p \neq 0.8 \)- \( H_0: \mu \geq 0.8 \) and \( H_a: \mu < 0.8 \)- \( H_0: p \geq 0.8 \) and \( H_a: p < 0.8 \)b. **Select the Test:**Choose the appropriate test.c. **Test Statistic Calculation:**Based on the sample of 200 people, 79% owned cats. Calculate the test statistic. Round to two decimal places.\[ z = \underline{\hspace{3cm}} \]d. **p-Value Calculation:**Calculate the p-value. Round to four decimal places.\[ \underline{\hspace{3cm}} \]e. **Decision:**Make a decision based on the p-value.- Options: - Fail to reject the null hypothesis - Reject the null hypothesisf. **Conclusion:**

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Description: **Title:** Testing a Veterinarian's Claim on Cat Ownership Proportion**Problem Statement:**The proportion of people that own cats is 80%. A veterinarian believes that this proportion is smaller than 80% and surveys 200 people. Test the veterinarian'

Given that, Sample size n=200 Population proportion p=0.80 Sample proportion of people who owned cats p^=0.79a. Yes, it is safe to assume that n≤0.05 of all subjects in the population. b. Verification: np1-p=200×0.80×1-0.80=32.0>10 Test the claim: a. Hypothesis: H0:p=0.8 H1:p<0.8 b. The test is one sample proportion z test. c. Test statistic: z=p^-pp1-pn=0.79-0.80.81-0.8200=-0.35 d. P-value: The left tailed p-value can be calculated as follows: Pz<-0.35=0.3632 e. Decision: Since the p-value is greater than significance level 0.005. Fail to reject the null hypothesis. f. Conclusion: There is not sufficient evidence that the proportion of people who own cats is smaller.

Math

Statistics

The proportion of people that own cats is 80%. A veterinarian believes that this proportion is smaller than 80% and surveys 200 people. Test the veterinarian's claim at the a = 0.005 significance level.

The proportion of people that own cats is 80%. A veterinarian believes that this proportion is smaller than 80% and surveys 200 people. Test the veterinarian's claim at the a = 0.005 significance level.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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