**Hypothesis Testing: Comparing Proportions of Cat Ownership Between Genders****Objective:**Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.05 significance level.**Null and Alternative Hypotheses:**- \( H_0: p_M = p_F \): The null hypothesis states that the proportion of men who own cats (\( p_M \)) is equal to the proportion of women who own cats (\( p_F \)).- \( H_1: p_M < p_F \): The alternative hypothesis suggests that the proportion of men who own cats is less than that of women.**Test Type:**- The test is left-tailed, which corresponds to the hypothesis that one proportion is less than another.**Sample Data:**- Men: 40% of 40 men owned cats.- Women: 65% of 40 women owned cats.**Statistical Analysis:**- **Test Statistic:** [To be calculated and filled in by user] (to 2 decimal places).- **P-value:** [To be calculated and filled in by user] (to 4 decimal places).**Conclusion:**- Based on the calculated test statistic and p-value, you will either: - Reject the null hypothesis - Fail to reject the null hypothesisSelect the appropriate option after performing the calculations.**Action:**Click "Check Answer" after filling in the test statistic and p-value to determine if the null hypothesis should be rejected or not.

Name: **Hypothesis Testing: Comparing Proportions of Cat Ownership Between
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Description: **Hypothesis Testing: Comparing Proportions of Cat Ownership Between Genders****Objective:**Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.05 significance level.**Null and Alterna

Given : The hypothesis of the proportion of men owns a cat is less than the proportion of women who owns a cat. The sample size of men nm=40 The proportion of men owns cat pm= 0.4 The sample size of women nw=40 Proportion women own cat pw= 0.65 level of significance α=0.05i)The null and alternate hypothesis: H0: pm=pw H0: The proportion of men who owns a cat is equal to the proportion of women who owns cats. H1: pm<pw H1: The proportion of men who owns a cat is smaller than the proportion of women who owns cats. ii) It a left tailed test Because the rejection region is located to the extreme left of the distribution. HINT: left tailed is used in the situation where the null hypothesis having less than symbol (<).iii) The number of men owns cat in the sample is xm= 40*0.4 =16 The number of women owns cat in the sample is xw= 40*0.65 =26 The pooled proportion is computed as p¯=xm+xwnm+nwp¯=16+2640+40p¯=0.525 The appropriate test statistic is z=p⏜m-p⏜wp¯(1-p¯)(1nm+1nw)z=0.4-0.650.525(1-0.525)(140+140)z=-2.239 Test statistic =-2.24 by using the excel formula "=NORM.S.DIST(-2.24, TRUE)" the p-value is calculated as 0.0125 iv) p-value =0.0125 iv) Decision rule: Since the p-value is less than the significance value (0.0125<0.05) the null hypothesis is rejected. Conclusion: There is enough evidence to claim that the proportion of men who owns a cat is smaller than the proportion of women who owns cats.

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Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .05 significance level. The null and alternative hypothesis would be: Ho: HM = HF Ho:PM = PF Ho:HM = HF Ho:HM = #F Ho:PM = PF Ho:PM = PF H1: HM < HF H1:PM > PF H1:HM > HF H1:HM + HF H1:PM PF H1:PM < PF The test is: right-tailed two-tailed left-tailed Based on a sample of 40 men, 40% owned cats Based on a sample of 40 women, 65% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 4 decimals) Based on this we: O Reject the null hypothesis Fail to reject the null hypothesis

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .05 significance level. The null and alternative hypothesis would be: Ho: HM = HF Ho:PM = PF Ho:HM = HF Ho:HM = #F Ho:PM = PF Ho:PM = PF H1: HM < HF H1:PM > PF H1:HM > HF H1:HM + HF H1:PM PF H1:PM < PF The test is: right-tailed two-tailed left-tailed Based on a sample of 40 men, 40% owned cats Based on a sample of 40 women, 65% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 4 decimals) Based on this we: O Reject the null hypothesis Fail to reject the null hypothesis

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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