A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Complete parts (a) through () below. Height (inches), x Head Circumference (inches), y 17.5 27.5 27.75 25.5 25 260 16.9 17.3 17.6 17.1 (a) Treating height as the explanatory variable, x, use technology to determine the estimates of y and B1- lo bo = 11.2571 (Round to four decimal places as needed.) P sb, = 0.2286 (Round to four decimal places as needed.) (b) Use technology to compute the standard error of the estimate, s . S, = 0.0756 (Round to four decimal places as needed.) (c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine Sp = 0.0310 (Round to four decimal places as needed.) (d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the a=0.01 level of significance. State the null and allemative hypotheses for this test. Choose the correct answer below. O A. Họ: Po "0 H: la #0 OB. Ho: lo =0 H: lo >0 c. Họ: "0 H: #0 O D. Ho: "0 H: >0 Determine the P.value for this hypolhesis test. P-value = 0.005 (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. Reject H, and conclude that a linear relation exists between a childs height and head circumference at the level of significance a =0.01. O B. Reject Hp and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance a = 0.01. OC. Do not reject Hy and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance a =0.01. O D. Do not reject Hg and conclude that a linear relation exists between a child's height and head circumference at the level of significance a =0.01. (e) Use technology to construct a 95% confidence interval about the slope of the true least-squares regression line. Lower bound: 0.130 Upper bound: 0.327 (Round to three decimal places as needed.) (f) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head circumference? A good estimate of the child's head circumference would be 17.31 inches. (Round to two decimal places as needed.)