The image displays content from an educational platform called "MyOpenMath," dated 11/15/2020. It presents a question regarding evidence to support a veterinarian's belief. The options are:- There is enough evidence to support the veterinarian's belief.- There is not enough evidence to support the veterinarian's belief.This question likely relates to a statistical or scientific study in veterinary medicine where students must evaluate the adequacy of evidence. No graphs or diagrams are present in the image. The URL at the bottom indicates the source: https://www.myopenmath.com/assess2/?cid=80488&aid=5754731#/print **Hypothesis Testing for Cat Ownership Proportions**A veterinarian is researching the proportion of men and women cat owners. The veterinarian believes that the proportion of male cat owners is significantly different from the proportion of female cat owners. To investigate, samples of men and women cat owners are taken. In a sample of 60 men, 45% owned cats. In another sample of 80 women, 70% owned cats. The belief is tested at a 0.1 significance level.**Preliminary Steps:**a. Assumption Check:Is it safe to assume:- \( n_{men} \leq 5\% \) of all men and- \( n_{women} \leq 5\% \) of all women?- ☐ Yes- ☐ Nob. Verification:Ensure \( n\hat{p}(1 - \hat{p}) \geq 10 \). Round to one decimal place.\[ n_{men}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_ \]\[ n_{women}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_ \]**Test the Claim:**a. Hypotheses:Determine the null and alternative hypotheses.\( H_0: p_{men} = p_{women} \)\( H_a: p_{men} \neq p_{women} \)b. Hypothesis Test Type:- ☐ Right-tailed- ☐ Two-tailed- ☐ Left-tailedc. Test Statistic:Calculate and round to two decimal places.\[ z = \_\_\_\_\_\_ \]d. P-value:Calculate and round to four decimal places.\[ \text{p-value} = \_\_\_\_\_\_ \]e. Decision:- ☐ Reject the null hypothesis.- ☐ Fail to reject the null hypothesis.f. Conclusion:Write the conclusion based on the decision.

Preliminary: a. A random sample of 60 men and another random sample of 80 women are considered. In general there would be a large number of men and women who have cats. It would be safe to assume that the samples sizes of nmen, nwomen are less than 5%. Thus, it is safe to assume that both sample size would be less than 5%. Correct answer: Yes. b. The pooled estimate is, p^=nmenp^men+nwomenp^womennmen+nwomen=60×0.45+80×0.7060+80=83140=0.5929 The pooled estimate is 0.5929. Conditions: nmenp^1-p^=60×0.5929×1-0.5929=14.5>10 nwomenp^1-p^=80×0.5929×1-0.5929=19.3>10Test the claim: a. Let pmen denotes the population proportion of men car owners, and pwomen denotes the population proportion of women car owners. The claim of the test is that the proportion of men car owners is significantly different than the proportion of women car owners. The hypothesis is, Null hypothesis: H0:pmen=pwomen Alternative hypothesis: Ha:pmen≠pwomen b. The alternative represents the not equal symbol indicating that the test is two tailed. Thus, the hypothesis test is two-tailed. c. The test statistic is, z=p^men-p^womenp^1-p^1nmen+1nwomen=0.45-0.700.59291-0.5929160+180=-0.250.08390=-2.98 Thus, the test statistic is -2.98. d. The hypothesis is two tail. The p-value for two tailed test is, p-value=Pz<-2.98 or z>-2.98=2×Pz<-2.98 The probability of z less than –2.98 can be obtained using the excel formula “=NORM.S.DIST(–2.98,TRUE)”. The probability value is 0.0014. The required p-value is, p-value=2×Pz<-2.98=2×0.0014=0.0028 Thus, the p-value is 0.0028. e. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.0028) is less than the level of significance (0.10). based on the decision rule, reject the null hypothesis. f. The null hypothesis is rejected. Thus, there is sufficient evidence that the proportion of men car owners is significantly different than the proportion of women car owners. Correct Answer: There is enough to support the veterinarian's belief.

Math

Statistics

A veterinarian is interested in researching the proportion of men and women cat owners and believes that the proportion of men cat owners is significantly different than the proportion of women cat owners. The veterinarian decides to obtain two independent samples of men and women cat owners and finds from one sample of 60 men, 45% owned cats. In the second sample of 80 women, 70% owned cats. Test the veterinarian's belief at the a = 0.1 significance level.

A veterinarian is interested in researching the proportion of men and women cat owners and believes that the proportion of men cat owners is significantly different than the proportion of women cat owners. The veterinarian decides to obtain two independent samples of men and women cat owners and finds from one sample of 60 men, 45% owned cats. In the second sample of 80 women, 70% owned cats. Test the veterinarian's belief at the a = 0.1 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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