3of 4日vthat its members utilize the club's facilities. A random sample of 300 members of this health clubwas selected, and a report of these members' activity over the past week was generated using thehealth club's information management system. The following results were obtained.Number of Days per Week Member Utilizes Club's FacilitiesSett0-12-34-56-7Male439132Female3568213(a) Is there enough evidence, at the 5% level of significance, to conclude that the number of daysper week a member utilizes the health club's facilities is independent of their gender?utions writtenIartleby | lot ofI have not .ed. Follow. You ha(b) Based on this result, what should the health club manager conclude about the relationshipbetween gender and the number of days per week that its members utilize the club's facilities?5:21 PM12/1/2020F6FBF12DELETEINSERTGender A health club manager was interested in whether gender is related to the number of days per weekthat its members utilize the club's facilities. A random sample of 300 members of this health clubwas selected, and a report of these members' activity over the past week was generated using thehealth club's information management system. The following results were obtained.SettNumber of Days per Week Member Utilizes Club's Facilities0- 12-34 - 56-7tions written IMale4391327Female3568213(a) Is there enough evidence, at the 5% level of significance, to conclude that the number of daysper week a member utilizes the health club's facilities is independent of their gender?rtleby | lot of1 have not ...ated. Follow. You haTA5:21 PMへ )12/1/20201001FSFBF11F12DELETEINSERTHOMEPPOUPGender

Name: 3of 4日vthat its members utilize the club's facilities. A random sampl
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Description: 3of 4日vthat its members utilize the club's facilities. A random sample of 300 members of this health clubwas selected, and a report of these members' activity over the past week was generated using thehealth club's information management system. The

(a) The test is to check whether the number of days per week a member utilizes the health club's facilities is independent of their gender or not. The hypothesis is, Null hypothesis: H0: The number of days per week a member utilizes the health club's facilities is independent of their gender. Alternative hypothesis: H1: The number of days per week a member utilizes the health club's facilities is dependent of their gender. The row and column totals are, 0-1 2-3 4-5 6-7 Total Male 43 91 32 7 173 Female 35 68 21 3 127 Total 78 159 53 10 300 The expected values are, 0-1 2-3 4-5 6-7 Total Male 173×78300=44.98 173×159300=91.69 173×53300=30.56 173×10300=5.77 173 Female 127×78300=33.02 127×159300=67.31 127×53300=22.44 127×10300=4.23 127 Total 78 159 53 10 300 The test statistic is, χ2=Sum ofObserved-Expected2Expected=43-44.98244.98+91-91.69291.69+32-30.56230.56+7-5.7725.77+35-33.02233.02+68-67.31267.31+21-22.44222.44+3-4.2324.23=0.087+0.005+0.068+0.264+0.119+0.007+0.092+0.359=1.001 The test statistic is 1.001. The degrees of freedom is, df=r-1c-1=2-14-1=3 The degrees of freedom is 3. Computation of P-value: The P-value of χ2-distribution for test statistic 1.001 at 3 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(1.001,3)”. The P-value is 0.8010. Decision rule: If P-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The P-value (0.8010) is greater than the level of significance (0.05). Based on decision rule, fail to reject the null hypothesis. Thus, it can be concluded that the number of days per week a member utilizes the health club's facilities is independent of their gender.(b) Based on the result obtained, the health club manager should conclude that there is no relation between gender and number of days per week that members utilize the club facilities.

Math

Statistics

(a) Is there enough evidence, at the 5% level of significance, to conclude that the number of days per week a member utilizes the health club's facilities is independent of their gender? (b) Based on this result, what should the health club manager conclude about the relationship between gender and the number of days per week that its members utilize the club's facilities?

(a) Is there enough evidence, at the 5% level of significance, to conclude that the number of days per week a member utilizes the health club's facilities is independent of their gender? (b) Based on this result, what should the health club manager conclude about the relationship between gender and the number of days per week that its members utilize the club's facilities?

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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