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##### 10 questions observations and correlations

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Question;The following sample observations were;randomly selected.;X: 4;5;3;6;10;Y: 4;6;5;7;7;(1);Fill in the blanks below: (Round your answers to 2 decimal places.);Sx;Sy;Coefficient of correlation;Coefficient of determination;(2);Choose the right option.;The correlation coefficient;obtained here indicates correlation between X and Y.;(3);Fill in the blanks. (Round your answer to the nearest whole number.);The coefficient of;determination obtained here indicates X accounts for approximately percent of;the variation in Y.;2.;The following sample observations were;randomly selected.;X: 5 3;6 3 4;4 6;8;Y: 13 15;7 12 13;11 9 5;Determine the coefficient of correlation and the;coefficient of determination. Interpret the association between X and Y.;(Round your coefficient of determination to 4;decimal places. Round all other answers to 2 decimal places. Negative amounts;should be indicated by a minus sign.);X;Y;()2;()2;()();5;13;2.38;0.02;5.64;0.30;3;15;4.38;3.52;19.14;6;7;1.13;1.27;13.14;-4.08;3;12;-1.88;3.52;1.89;4;13;-0.88;2.38;5.64;-2.08;4;11;-0.88;0.38;0.14;-0.33;6;9;1.13;-1.63;1.27;8;5;3.13;-5.63;9.77;-17.58;39;85;=;=;sx;=;sy;=;r;=;The correlation coefficient of indicates;a relationship between X and Y. The coefficient of;determination is;found by squaring the value of.;X accounts for percent;of the variation in Y.;3.;Bi-lo Appliance Super-Store has outlets in several large;metropolitan areas in New England. The;general sales manager aired a commercial for a digital camera on selected;local TV stations prior to a sale starting on Saturday and ending Sunday. She;obtained the information for Saturday?Sunday digital camera sales at the;various outlets and paired it with the number of times the advertisement was;shown on the local TV stations. The purpose is to find whether there is any;relationship between the number of times the advertisement was aired and;digital camera sales. The pairings are;Location of;Number;of;Saturday?Sunday;Sales;TV Station;Airings;($;thousands);Providence;4;15;Springfield;2;8;New Haven;5;21;Boston;6;24;Hartford;3;17;(a);What is the dependent variable?;is the dependent variable.;(c);Determine the correlation coefficient. (Round your answer to 2 decimal places.);Coefficient of correlation;(d);Interpret these statistical measures.;The statistical measures;obtained here indicate correlation between the variables.;4.;The production department of Celltronics International;wants to explore the relationship between the number of employees who;assemble a subassembly and the number produced. As an experiment, two;employees were assigned to assemble the subassemblies. They produced 15;during a one-hour period. Then four employees assembled them. They produced;25 during a one-hour period. The complete set of paired observations follows.;Number;of;Assemblers;One-Hour;Production (units);2;15;4;25;1;10;5;40;3;30;The dependent variable is production, that is, it is;assumed that different levels of production result from a different number of;employees.;(b);A scatter diagram is provided below. Based on it, does;there appear to be any relationship between the number of assemblers and;production?, as the number of;assemblers, so does the production.;(c);Compute the coefficient of correlation. (Negative amounts should be indicated by a minus sign.;Round sx, sy and r to 3;decimal places.);X;Y;()2;()2;()();2;15;?9;81;4;25;1;1;1;1;10;?14;196;5;40;2;4;32;3;30;6;0;0;=;=;sx;=;sy;=;r;=;(d);Evaluate the strength of the relationship by computing;the coefficient of determination. (Round your;The r2 is;so about percent;of the variation in production is explained by;the variation in the number of assemblers.;5.;The owner of Maumee Ford-Mercury-Volvo wants to study the;relationship between the age of a car and its selling price. Listed below is;a random sample of 12 used cars sold at the dealership during the last year.;Car;Age;(years);Selling;Price ($000);Car;Age;(years);Selling;Price ($000);1;9;8.1;7;8;7.6;2;7;6.0;8;11;8.0;3;11;3.6;9;10;8.0;4;12;4.0;10;12;6.0;5;8;5.0;11;6;8.6;6;7;10.0;12;6;8.0;(a);If we want to estimate selling price on the basis of the;age of the car, which variable is the dependent variable and which is the;independent variable?;is the independent;variable and is the dependent variable.;(b-1);Determine the coefficient of correlation. (Negative amounts should be indicated by a minus sign.;Round your answers to 3 decimal places.);X;Y;()2;()2;()();9.0;8.1;1.192;0.007;1.420;0.099;7.0;6.0;-0.908;3.674;0.825;1.741;11.0;3.6;2.083;4.340;10.945;-6.892;12.0;4.0;3.083;9.507;8.458;-8.967;8.0;5.0;-0.917;-1.908;3.642;1.749;7.0;10.0;-1.917;3.092;9.558;-5.926;8.0;7.6;-0.917;0.692;0.840;-0.634;11.0;8.0;2.083;1.092;4.340;2.274;10.0;8.0;1.083;1.092;1.174;1.192;12.0;6.0;3.083;-0.908;9.507;0.825;6.0;8.6;-2.917;1.692;8.507;2.862;-4.934;6.0;8.0;-2.917;1.092;8.507;1.192;-3.184;107.000;82.900;=;=;sx;=;sy;=;r;=;Determine the coefficient of;determination. (Round your answer to 3 decimal;places.);(c);Interpret these statistical measures.;Does it surprise you that the relationship is inverse? (Round your answer to nearest whole number.);correlation between age of;car and selling price. So, percent;of the variation in the selling price is explained by the variation in;the age of the car.;6.;The following hypotheses are given.;H0:?? 0;H1:? > 0;A random sample of 12 paired observations;indicated a correlation of.32.;(1);State the decision rule for.05;significance level. (Round your answer to 3;decimal places.);Reject Ho;if t >;(2);Compute the value of the test statistic. (Round your answer to 2 decimal places.);Value of the test statistic;(3);Can we conclude that the correlation in the population is;greater than zero? Use the.05 significance level.;Ho. We conclude that the correlation in the population is;7.;The following hypotheses are given.;A random sample of 15 paired observations have a;correlation of?.46. Can we conclude that the correlation in the population;is less than zero? Use the.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer;to 3 decimal places.);Reject H0 if t;

Paper#60840 | Written in 18-Jul-2015

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