Question

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. A normal probability plot suggests that the residuals are normally distributed. Complete parts​ (a) and​ (b) below. Height​ (inches), x 27.75 24.5 27.5 27 26.5 Head Circumference​ (inches), y 17.6 17.1 17.5 17.5 17.3 ​(a) Use technology to determine s Subscript b 1. s Subscript b 1equals nothing   ​(Round to four decimal places as​ needed.) ​(b) Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 B. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 C. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) What is the conclusion that can be​ drawn? A. Do not reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01. B. Do not reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01. C. Reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01. D. Reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01.

Answer 1

Since here it is said to use technology, I have used R software for this problem.

(a) From this question, all I can understand is that the standard deviation of , which is the ordinary least square estimate of , the regression coefficient corresponding to the variable 'Height', is required.

The required standard deviation is, = 0.0231.

(b) The null and alternative hypotheses are:

C. vs.

The r output is provided below:

The p-value for this hypothesis testing problem is given by, p-value = 0.008

The conclusion will be:

C. Reject and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance .