Unit 4 Section 3 Solutions

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Jan 9, 2024

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X2-Test Obseri...•ed: [ A 1 Expected: [ B 1 C.a 1 c.1...1 l .ate Dr .a1 .• J MATRIX[A1 .-.. •x7 L • ,_j X2-Test ..... 2 -10c: .-, ... c, 1--,4--, •• ._ - ,_I ■ ..::.t,c, L ( P=1.384577E-23 df=2 'ti 1Bti ] ] Elementary Statistics Unit 4 : Section 3 Solutions Your solutions should be clear, complete, and sufficiently detailed in order to demonstrate your understanding and communicate your reasoning and method of solving the problem. Exercise 1 A CBS News poll asked a random sample of 1025 Americans how they identified themselves politically and whether they thought the news media was too liberal. The results of this poll are summarized in the table below. Political Identification Conservative Moderate Liberal Is the news media too liberal? Yes 232 165 41 No 154 247 186 (a) Is a person’s response to this question independent of their political identification? Use ! = 0.05. H 0 : The events are independent. H 1 : The events are not independent. Use ! = 0.05 p-value ! 1.4 E " 23 ! 0.000 Since the p-value of 0.000 is 0.05 or less, the decision is to reject H 0 . Therefore, a person’s response to this question is not independent of their political identification. (b) Based on this result, does a person’s response to this question depend on how they identify themselves politically? Based on this result, a person’s response to this question does depend on how they identify themselves politically. Page 1 Mathematics 13

X2-Test Obseri...•ed: [ A 1 Expected: [ B 1 C.a 1 c.1...1 l .ate Dr .a1 .• J MATRIX[A] 3 x4 [ 102 19B 91 [ '19 126 213 [ ti 3 11 X2-Test ..... 2 _..., 1 C: .::,c:~.::, .... , 1 .... , .... -L ._,. c,._,._,c, ( ( P=7.965343E-44 df=6 Elementary Statistics Unit 4 : Section 3 Solutions Exercise 2 In a recent Gallup poll, a random sample of 1014 adults nationwide were asked “How often do you worry about your weight?” and “How would you describe your own personal weight situation?”. The poll results are presented in the table below. How often do you worry about your weight? All of the time Some of the time Not too often Never How would you describe your own personal weight situation? Overweight 102 198 91 25 About right 49 126 213 159 Underweight 6 3 11 31 (a) Is how often a person worries about their weight independent of how they describe their own personal weight situation? H 0 : The events are independent. H 1 : The events are not independent. Use ! = 0.05 p-value ! 8.0 E " 44 ! 0.000 Since the p-value of 0.000 is 0.05 or less, the decision is to reject H 0 . Therefore, how often a person worries about their weight is not independent of how they describe their own personal weight situation. (b) Based on this conclusion, does a person’s personal weight situation affect how often they worry about their weight? Based on this conclusion, a person’s personal weight situation does affect how often they worry about their weight. The data indicate that an overweight person is more likely to worry about their weight either some or all of the time while an underweight person is more likely to worry about their weight either never or not too of often. Page 2 Mathematics 13

X2-Test Obseri...•ed: [ A 1 Expected: [ B 1 C.a 1 c.1...1 l .ate Dr .a1 .• J MATRIX[A] 2 x4 X2-Test 91 tiB ){ 2 = 1. 000771633 p=. 8010E.52443 df=3 32 21 Elementary Statistics Unit 4 : Section 3 Solutions Exercise 3 A health club manager was interested in whether gender is related to the number of days per week that its members utilize the club’s facilities. A random sample of 300 members of this health club was selected, and a report of these members’ activity over the past week was generated using the health club’s information management system. The following results were obtained. Number of Days per Week Member Utilizes Club’s Facilities 0 - 1 2 - 3 4 - 5 6 - 7 Gender Male 43 91 32 7 Female 35 68 21 3 (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? H 0 : The events are independent. H 1 : The events are not independent. Use ! = 5% p-value ! 0.801 Since the p-value of 0.801 is not 0.05 or less, the decision is to not reject H 0 . Therefore, there is 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? Based on this result, the health club manager should conclude that there is no relationship between gender and the number of days per week that its members utilize the club’s facilities. In other words, there are no gender differences in how frequently the members utilize the club’s facilities. Page 3 Mathematics 13

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X2-Test Obseri...•ed: [ A 1 Expected: [ B 1 C.a 1 c.1...1 l .ate Dr .a1 .• J MATRIX[A1 [ 37 12 [ 'tli 22 X2-Test •.,,.. 2 -o oo~c,...,q.-,40 .... -u. c:,c;,._,c, ( _. .L o p=.011773081 df=2 .-.. •x7 L • ,_j ~ 2B ] ] Elementary Statistics Unit 4 : Section 3 Solutions Exercise 4 A music industry marketing firm asked a random sample of 150 consumers if they have purchased any music from an online music store in the last year. The results, grouped by age, are displayed in the following table. Consumer’s Age 18 to 29 30 to 49 50 to 69 Have you purchased any music from an online music store in the last year? Yes 37 12 5 No 46 22 28 (a) Is purchasing music online independent of the consumer’s age? Use ! = 5%. H 0 : The events are independent. H 1 : The events are not independent. Use ! = 5% p-value ! 0.012 Since the p-value of 0.012 is 0.05 or less, the decision is to reject H 0 . Therefore, purchasing music online is not independent of the consumer’s age. (b) Based on this result, what should the music industry marketing firm report about the association between purchasing music online and the consumer’s age? Based on this result, the music industry marketing firm should report that there is an association between purchasing music online and the consumer’s age. The data indicate that consumers who purchase music online tend to be younger (18 to 29) rather than older (50 to 69). Page 4 Mathematics 13

Unit 4 Section 3 Solutions

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