Question

he data in the accompanying table represent the heights and weights of a random sample of professional baseball players. Complete parts ​(a) through ​(c) below. LOADING... Click the icon to view the data table. ​(a) Draw a scatter diagram of the​ data, treating height as the explanatory variable and weight as the response variable. Choose the correct graph below. A. 70 76 82 180 210 240 Height (inches) Weight (pounds) A scatter diagram has a horizontal axis labeled “Height (inches)” from less than 70 to 82 plus in increments of 6 and a vertical axis labeled “Weight (pounds)” from less than 180 to 240 plus in increments of 30. The following 9 approximate points are plotted, listed here from left to right: (69, 186); (71, 200); (72, 180); (74, 190); (75, 230); (76, 218); (77, 198); (78, 228); (82, 232). B. 70 76 82 180 210 240 Height (inches) Weight (pounds) A scatter diagram has a horizontal axis labeled “Height (inches)” from less than 70 to 82 plus in increments of 6 and a vertical axis labeled “Weight (pounds)” from less than 180 to 240 plus in increments of 30. The following 9 approximate points are plotted, listed here from left to right: (69, 186); (71, 198); (72, 228); (74, 232); (75, 180); (75, 200); (75, 228); (76, 230); (82, 190). C. 70 76 82 180 210 240 Height (inches) Weight (pounds) A scatter diagram has a horizontal axis labeled “Height (inches)” from less than 70 to 82 plus in increments of 6 and a vertical axis labeled “Weight (pounds)” from less than 180 to 240 plus in increments of 30. The following 9 approximate points are plotted, listed here from left to right: (69, 186); (71, 200); (72, 180); (74, 190); (75, 198); (75, 228); (75, 230); (76, 228); (82, 232). ​(b) Determine the​ least-squares regression line. Test whether there is a linear relation between height and weight at the alphaequals0.05 level of significance. Determine the​ least-squares regression line. Choose the correct answer below. A. ModifyingAbove y with caretequals4.160xnegative 101.7 B. ModifyingAbove y with caretequals8.160xnegative 101.7 C. ModifyingAbove y with caretequals4.160xnegative 103.7 D. ModifyingAbove y with caretequalsnegative 101.7xplus4.160 Test whether there is a linear relation between height and weight at the alphaequals0.05 level of significance. State the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 B. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 C. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) State the appropriate conclusion at the alphaequals0.05 level of significance. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. B. Do not reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. C. Do not reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. D. Reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. ​(c) Remove the values listed for Player 4 from the data table. Test whether there is a linear relation between height and weight. Do you think that Player 4 is​ influential? Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) State the appropriate conclusion at the alphaequals0.05 level of significance. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. B. Reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. C. Do not reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. D. Do not reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players. Do you think that Player 4 is​ influential? No Yes Player Height​ (inches) Weight​ (pounds) Player 1 76 227 Player 2 75 197 Player 3 72 180 Player 4 82 231 Player 5 69 185 Player 6 74 190 Player 7 75 228 Player 8 71 200 Player 9 75 230

Answer 1

A)Scatter plot is C)70 76 82 180 210 240 Height (inches) Weight (pounds) A scatter diagram has a horizontal axis labeled “Height (inches)” from less than 70 to 82 plus in increments of 6 and a vertical axis labeled “Weight (pounds)” from less than 180 to 240 plus in increments of 30. The following 9 approximate points are plotted, listed here from left to right: (69, 186); (71, 200); (72, 180); (74, 190); (75, 198); (75, 228); (75, 230); (76, 228); (82, 232)

B)The least square regression line is y^ = 4.16x - 101.7 (A)

The null and alternative hypothesis are (D)

p value is .028

The conclusion is A). Reject H₀. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players

C)After removing values of Player 4 , p value is .053

The conclusion is D)Do not reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players

The player 4 is influential because it makes the regression coefficient significant and also increases the fit of the model