Question

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. 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. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of

alphaαequals=0.05

Shoe Print	28.6	29.4	32.2	32.4	27.3
Foot Length (c	25.1	25.8	26.8	27.7	25.0
Height (cm)	172.5	176.7	188.4	170.1	179.2

Answer 1

CORRELATION 28.6 172.5 817.96 29756.25 4933.5 29.4 176.7 864.36 31222.89 5194.98 32.2 188.4 1036.84 35494.56 6066.48 32.4 170.1 1049.76 28934.01 5511.24 27.3 179.2 745.29 32112.64 4892.16 calculation procedure for correlation sum of (x)x 149.9 sum of (v)y 886.9 sum of (xA2)- xA2 4514.21 sum of (y^2)= yy^2 = 157520.35 sum of (x*y-yy = 26598.36 to caluclate value of r xy) covariance (xy) /sd (x) * sd (y) covariance ( x,y )-ΙΣΧ"y-N *(3x/N) * (Zy/N) l/n-1 26598.36 5 (149.9/5) * (886.9/5) 1/5- 1 and now to calculate r( xy) 1.82/ (SQRT(1/5*26598.36-(1/5*149.9)A2)) SQRT(1/5*26598.36-(1/5*886.9)A2) -1.82 (2.01*6.357) -0.142 value of correlation is 0.142 coeffcient of determinationA20.02 properties of correlation 1. If r -1 Corrlation is called Perfect Positive Corrlelation 2. If r =-1 Correlation is called Perfect Negative Correlation 3. If r 0 Correlation is called Zero Correlation & with above we conclude that correlation (r) is0.1424> 0 ,positive correlation

Given that, value of r -0.142 number (n) 5 null, Ho: p -0 alternate, HI: pl-0 level of significance, a 0.05 from standard normal table, two tailed t a/2 3.182 since our test is two-tailed reject Ho, if to < -3.182 OR if to 3.18.2 we use test statistic (t)sqrt(1-rA2/(n-2)) to 0.142/(sqrt (1-0.142A2 )/(5-2) ) to 0.25 to |0.25 critical value the value of It at los 0.05% is 3.182 we got Ito0.25 & t al 3.182 make decision hence value of Ito l < l t α 1 and here we do not reject Ho ANSWERS null, Ho: ρ-0 alternate, H1: p! 0 test statistic: 0.25 crit tical value: -3.182, 3.182 decision: do not reject Ho they don't appear to be correlated