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 oflinear 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 a -0.05.Shoe Print (cm)Foot Length (cm)Height (cm)Construct a scatterplot. Choose the correct graph belowCOA200-15030.9 31.8 32.1 27.730.926.7 26.3 27.6 27.4 25.6179.6 1848 189.4 178.9 1742535Shoe Print (m)QThe linear correlation coefficient is r-(Round to three decimal places as needed.)Determine the null and alternative hypotheses.Ho: PLH₁: P(Type integers or decimals. Do not round)The test statistic is t-(Round to two decimal places as needed)The P-value is(Round to three decimal places as needed.)OBOA. Yes, because shoe print length and height appear to be correlated.OB. No, because shoe print length and height appear to be correlatedOC. No, because shoe print length and height do not appear to be correlatedOD. Yes, because shoe print length and height do not appear to be correlated200-160-Shee PretBecause the P-value of the linear correlation coefficient isthe significance level, thereBased on these results, does it appear that police can use a shoe print length to estimate the height of a male?QaOc.QQLsufficientsufficientcient evidence to support the claim that there is a linear correlation between shoe print lengths and heights of malesOD.200aQ

Let x denote the shoe print length (in cm) and y denote the height (in cm ) of the male. The data on x and y is given as followsShoe Print (cm)xHeight (in cm )y30.9179.630.9184.631.8189.432.1178.927.7174Here the sample size is n=5The defined level of significance is α=0.05To find:The scatter plot for x and yThe correlation coefficient (r) valueHypothesis testing for checking the significance of rThe steps involved in obtaining the scatter plot using Excel is as followsEnter the values of x and y in ExcelSelect these variables and go to Insert→Chart→ScatterTo the resultant graph provide the axis labels.The Excel output is as followsHence the correct option that matches the obtained plot is (D)The formula to compute the linear correlation between the x and y is given as follows xiyi(xi−x¯)(yi−y¯)(xi−x¯)∗(yi−y¯)(xi−x¯)2(yi−y¯)230.9179.60.22-1.7-0.3740.04842.8930.9184.60.223.30.7260.048410.8931.8189.41.128.19.0721.254465.6132.1178.91.42-2.4-3.4082.01645.7627.7174-2.98-7.321.7548.880453.29SUM 153.4906.50027.7712.248138.44Thus the value of r is∴ The linear correlation coefficient is, r = 0.674.The null and alternative hypotheses for testing the significance of the correlation coefficient are given as followsH0:ρ=0 ( There is no significant correlation between x and y)H1:ρ≠0 ( There is a significant correlation between x and y)To test the above hypothesis, the t-test statistic is given asThus the t-test statistic is 1.58.The above test statistic follows t-distribution with (n−2) degrees of freedomThe P-value can be computed using the Excel function = T.DIST.2T (x, deg_freedom)Here, x=t=1.58 and deg_freedom=n−2=3∴P−value=0.212Decision: Since P−value=0.212>α=0.05, there is no sufficient evidence to reject the null hypothesis. Hence the test fails to reject the null hypothesis.Conclusion:Because the P-value of the linear correlation coefficient is greater than the significance level, there is no sufficient evidence to claim that there is a linear correlation between shoe print lengths and height of malesBased on the above results, the respective variables can not be used and hence the correct reason isC) No, because the shoe print lengths and height do not appear to be correlated. A.)The correct scatterplot is Option (D)The null and alternative hypotheses for testing the significance of the correlation coefficient areH0:ρ=0H1:ρ≠0The t-test statistic is 1.58.P−value=0.212Because the P-value of the linear correlation coefficient is greater than the significance level, there is no sufficient evidence to claim that there is a linear correlation between shoe print lengths and height of malesBased on the above results, the respective variables can not be used and hence the correct reason isC) No, because the shoe print lengths and height do not appear to be correlated.