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The heights (in metres) of the winners and runners-up in elections to a particular post were recorded. Winner 1.78 1.87 1.87 1.90 1.91 1.91 1.82 1.82 Runner-up 1.85 1.78 1.79 1.74 1.90 1.90 1.87 1.95 (a) Plot a scatter graph of these data. (b) The following output was obtained from an analysis carried out in R: > winner<-c(1.78, 1.87, 1.87, 1.90, 1.91, 1.91, 1.82, 1.82) > runnerup<-c(1.85, 1.78, 1.79, 1.74, 1.90, 1.90, 1.87, 1.95) > cor.test (winner,runnerup) Pearson's product-moment correlation data: winner and runnerup

The heights (in metres) of the winners and runners-up in elections to a particular post were recorded. Winner 1.78 1.87 1.87 1.90 1.91 1.91 1.82 1.82 Runner-up 1.85 1.78 1.79 1.74 1.90 1.90 1.87 1.95 (a) Plot a scatter graph of these data. (b) The following output was obtained from an analysis carried out in R: > winner<-c(1.78, 1.87, 1.87, 1.90, 1.91, 1.91, 1.82, 1.82) > runnerup<-c(1.85, 1.78, 1.79, 1.74, 1.90, 1.90, 1.87, 1.95) > cor.test (winner,runnerup) Pearson's product-moment correlation data: winner and runnerup

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 23PFA
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The heights (in metres) of the winners and runners-up in elections to a particular post were recorded. Winner 1.78 1.87 1.87 1.90 1.91 1.91 1.82 1.82 Runner-up 1.85 1.78 1.79 1.74 1.90 1.90 1.87 1.95 (a) Plot a scatter graph of these data. (b) The following output was obtained from an analysis carried out in R: > winner<-c(1.78, 1.87, 1.87, 1.90, 1.91, 1.91, 1.82, 1.82) > runnerup<-c(1.85, 1.78, 1.79, 1.74, 1.90, 1.90, 1.87, 1.95) > cor.test(winner, runnerup) Pearson's product-moment correlation data: winner and runnerup t = -0.56964, df = 6, p-value = 0.5896 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.8030109 0.5689796 sample estimates: cor -0.2265121 (i) Explain clearly which analysis is being carried out. (ii) What can you conclude from the p-value? (iii) Interpret the confidence interval.
Transcribed Image Text:The heights (in metres) of the winners and runners-up in elections to a particular post were recorded. Winner 1.78 1.87 1.87 1.90 1.91 1.91 1.82 1.82 Runner-up 1.85 1.78 1.79 1.74 1.90 1.90 1.87 1.95 (a) Plot a scatter graph of these data. (b) The following output was obtained from an analysis carried out in R: > winner<-c(1.78, 1.87, 1.87, 1.90, 1.91, 1.91, 1.82, 1.82) > runnerup<-c(1.85, 1.78, 1.79, 1.74, 1.90, 1.90, 1.87, 1.95) > cor.test(winner, runnerup) Pearson's product-moment correlation data: winner and runnerup t = -0.56964, df = 6, p-value = 0.5896 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.8030109 0.5689796 sample estimates: cor -0.2265121 (i) Explain clearly which analysis is being carried out. (ii) What can you conclude from the p-value? (iii) Interpret the confidence interval.
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