Question

12. Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. The accompanying table lists the heights (cm) from several recent presidential elections. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.01. 5 Click the icon to view the heights of the candidates. Construct a scatterplot. Choose the correct graph below. OA. OB. OC. OD 2007 200 2007 200 Opponent H Opponent Height (cm) Opponent Height (cm) . Opponent Height (cm) 160+ 160 200 President Height (cm) 160+ 160 200 President Height (cm) 160+ 160 200 President Height (cm) 160+ 160 200 President Height (cm) The linear correlation coefficient r is (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: P(1) H:P(2) (Type integers or decimals. Do not round.) The test statistic is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) Because the P-value of the linear correlation coefficient is (3) the significance level, there (4) sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candiates and the heights of their opponents. Should we expect that there would be a correlation? O A. Yes, because height is the main reason presidential candidates are nominated. O B. No, because height is the main reason presidential candidates are nominated. O C. No, because presidential candidates are nominated for reasons other than height. OD. Yes, because presidential candidates are nominated for reasons other than height. 5: Candidate Heights President Opponent 183 177 189 173 183 186 198 180 180 180 190 190 185 185 176 179 185 178 183 177 175 178 182 178 171 186 182 170 (1) (2) > (3) O greater than less than or equal to (4) O is not O is Oooo * A v 0000 Ah

Answer 1

Oc. 2007 Opponent Height (cm) 160 160 200 President Height (cm)

S.No х Y (x-x)2 (y-7)2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 183 177 189 173 183 186 198 180 180 180 190 190 185 185 2579 176 179 185 178 183 177 175 178 182 178 171 186 182 170 2500 178.57 1.4745 52.0459 22.9031 125.7602 1.4745 3.1888 190.0459 17.7602 17.7602 17.7602 33.4745 33.4745 0.6173 0.6173 518.3571 6.61 0.18 41.33 0.33 19.61 2.47 12.76 0.33 11.76 0.33 57.33 55.18 11.76 73.47 293.4286 (x-x)(y-7) 3.1224 -3.0918 30.7653 6.4082 -5.3776 -2.8061 -49.2347 2.4082 - 14.4490 2.4082 -43.8061 42.9796 2.6939 -6.7347 -34.7143 SXY Mean 184.214 SSX SSY

correlation r='Sxy/(√Sxx*Syy) =

-0.089

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

test stat t=	r*(√(n-2)/(1-r2))=	-0.31
P value    =	0.762	(from excel:tdist(0.3096,12,2)

3) greater than

4) is not