1. In this section we use rto denote the value of the linear correlation coefcient. Why do we refer to this correlation coefcient as being linear? Choose the correct answer below. 0 A. The term linear refers to a straight line, and r measures the fraction of the points the best line passes through. 0 B. The term linear refers to a straight line that passes through the average values ofthe paired data, and rmeasures how well a scatterplot ts a straight-line pattern. 0 C. The term linear refers to the straight line that passes through the greatest number of points, and r measures the fraction of the points the line passes through. 0 D. The term linear refers to a straight line, and r measures how well a scatterplot ts a straightline pattern. 2. What is a scatterplot and how does it help us? Choose the correct answer below. 0 A. Ascatterplot is a graph of paired (x, y} quantitative data. It provides a visual image of the data plotted as points, which helps show any patterns in the data. C) B. Ascatterplot is a formula that fits a straight line to data points, which helps plot the data. 0 C. A scatterplot is a table of paired (x, v) quantitative data sorted from least to greatest, which helps show the range of the data. 0 D. Ascatterplot is a graph of paired (x. v) qualitative data. It provides an organized display of the data, which helps show patterns in the data. 3. The table provided below shows paired data for the heights of a certain country's presidents and their main opponents in the election campaign. Construct a scatterplot Does there appear to be a correlation? ' Click the icon to View the data table for election heights. Construct a scatterplot Choose the correct graph below O A. O B A E 200 Q E 200$ Q E a 3 . a E 2 E 8: l3 g 13' O 160-,......1,) O 16 160 200 160 200 Presidents height President's height Does there appear to be a correlation between the preSident's height and his opponent's height? 0 A. Yes, there appears to be a correlation. As the president's height increases. his opponent's height increases. 0 E. Yes, there appears to be a correlation As the president's height increases. his opponent's height decreases. O C. Yes, there appears to be a correlation The candidate With the highest height usually wins. 0 D. No, there does not appear to he a correlation because there is no general pattern to the data. 1: Data table for election heights Ounuhent's heinht Q00: 16 1 60 200 President's height 9119 l3. 0 .0 Opponents height m D m 1 60 200 President's height ,09 LK'. President's Opponenl's height (cm) height (cm) President's Opponenl's q height(cm) height(cm) 181 175 181 171 186 183 170 187 184 170 175 190 185 190 184 192 176 190 192 172 187 180 172 176 183 170 176 184 179 181 185 194 4. The table lists weights (pounds) and highway mileage amounts (mpg) for seven automobiles. Use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation Print Weight (lb) 2905 3010 3510 3855 4155 2645 3115 9 Highway (mpg) 34 32 29 25 24 36 31 Which scatterplot below shows the data? O A. O B O C. OD 40- 40- 40- 40- Highway (mpg) Highway (mpg) Highway (mpg) Highway (mpg) 20- 20- 20-+ 20- 2500 4500 2500 4500 2500 4500 2500 4500 Weight (Ib) Weight (lb) Weight (lb) Weight (lb) Is there a linear relationship between weight and highway mileage? O A. Yes, as the weight increases the highway mileage decreases. O B. No, there appears to be no relationship O C. Yes, as the weight increases the highway mileage increases. O D. No, there appears to be a relationship, but it is not linear.5 Construd a scatterdiagram using the data table to the right This data is from a study comparing the amount of tar and carbon monoxide (CO) in cigarettes Use tar for Full dam the horizontal scale and use carbon monoxide (CO) for the vertical scale Determine whether there appears to be a relationship between cigarette tar and CO, Tar col Tar col Tar 16 15 12 11 2 3 16 16 8 11 13 13 1 1 10 9 6 7 10 10 18 18 11 11 I 5 7 12 12 9 8 Construct a scatterdiagram. O A. O B. O c. O D. 2 CO Q CO Q EU a 2 CO 16 16 12 Q Q Q 12 B . . . B . 4 Tar r3,- Tar r3,- Tar l3- 4 Tar r3,- D D D D 4 3121620 D 4 8121620 D 4 3121620 Is there a relationship between cigarette tar and CO? 0 A. Yes, as the amount eftar Increases the amount of carbon monoxide decreases. O B. No, there appears to be no relationship 0 (I. Yes, as the amount oftar Increases the amount 01 carbon monoxide also increases D D 4 3121620 6. For a data set of brain volumes (cm") and IQ scores of twelve males, the linear correlation coefficient is r= 0.679. Use the table available below to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical what do you conclude about a linear correlation? Print Click the icon to view the table of critical values of r. The critical values are (Type integers or decimals. Do not round. Use a comma to separate answers as needed.) Since the correlation coefficient r is (1) there (2) sufficient evidence to support the claim of a linear correlation. 2: Table of Critical Values of r Number of Pairs of Data n Critical Value of r 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 (1) O between the critical values ) O is in the right tail above the positive critical value O is not O in the left tail below the negative critical value7. For a data set of chest sizes (distance around chest in inches) and weights (pounds) of nine anesthetized bears that were measured, the linear correlation coefficient is r = 0.276. Use the table available below to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? Click the icon to view the table of critical values of r. The critical values are (Type integers or decimals. Do not round. Use a comma to separate answers as needed.) Since the correlation coefficient r is (1) there (2) sufficient evidence to support the claim of a linear correlation. 3: Table of Critical Values of r Number of Pairs of Data n Critical Value of r 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 .666 10 0.632 11 0.602 12 0.576 (1) O in the left tail below the negative critical value (2) O is not O in the right tail above the positive critical value O is O between the critical values 8. For a data set of brain volumes (cm) and IQ scores of eleven males, the linear correlation coefficient is found and the P-value is 0.607. Write a statement that interprets the P-value and includes a conclusion about linear correlation. The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is %, which is (1) so there (2) sufficient evidence to conclude that there is a linear correlation between brain volume and IQ score in males. (Type an integer or a decimal. Do not round.) (1) O low, (2) O is O high, O is not9. Twenty different statistics students are randomly selected. For each of them, their body temperature ( C) is measured and their head circumference (cm) is measured. If it is found that r= 0, does that indicate that there is no association betwen these two variables? Choose the correct answer below. O A. Yes, because if r= 0, the variables are completely unrelated. O B. No, because r does not measure the strength of the relationship, only its direction. O C. No, because while there is no linear correlation, there may be a relationship that is not linear. O D. No, because if r = 0, the variables are in a perfect linear relationship.10. Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim Correlation Results that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest Correlation coeff, r: 0.972661 size can be used to predict the weight? Use a significance level of a = 0.05. Critical r: 1 0.2680855 P-value (two tailed): 0.000 Determine the null and alternative hypotheses. Ho: P (1) Hy : p ( 2 ) (Type integers or decimals. Do not round.) Identify the correlation coefficient, r. r= (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.) O A. There are two critical values at r = + O B. There is one critical value at r= Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? Choose the correct answer below and, if necessary, fill in the answer box within your choice. (Round to three decimal places as needed.) O A. No, because the absolute value of the test statistic exceeds the critical value. O B. No, because the test statistic falls between the critical values. O C. Yes, because the absolute value of the test statistic exceeds the critical value. O D. Yes, because the test statistic falls between the critical values O E. The answer cannot be determined from the given information. When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? O A. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is too much variance in the weight of the bears. O B. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is not a linear correlation between the two. O C. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation between the two. O D. No, it is easier to measure weight than chest size because the chest is not a flat surface\f11. Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. Find the value of the correlation coefficient r and A determine whether there is a linear correlation. c. Remove the point with coordinates (10,1) and find the correlation coefficient r and determine whether there is a linear correlation. d. What do you conclude about the possible effect 10- ... ... ... from a single pair of values? Click here to view a table of critical values for the correlation coefficient.* 10 08 a. Do the data points appear to have a strong linear correlation? O No O Yes Acti b. What is the value of the correlation coefficient for all 10 data points? r= (Simplify your answer. Round to three decimal places as needed.) Is there a linear correlation between x and y? Use a = 0.01. O A. Yes, because the correlation coefficient is in the critical region. O B. No, because the correlation coefficient is in the critical region. O C. No, because the correlation coefficient is not in the critical region. O D. Yes, because the correlation coefficient is not in the critical region. c. What is the correlation coefficient when the point (10, 1) is excluded? r= (Round to three decimal places as needed.) Is there a linear correlation between x and y? Use a = 0.01. Pr O A. No, because the correlation coefficient is in the critical region. G O B. No, because the correlation coefficient is not in the critical region. O C. Yes, because the correlation coefficient is in the critical region. O D. Yes, because the correlation coefficient is not in the critical region. d. What do you conclude about the possible effect from a single pair of values? U O The effect from a single pair of values can change the conclusion. A single pair of values does not change the conclusion. PYR4: Table of Critical Values n a =.05 a = .01 950 990 878 959 .811 917 754 875 707 834 666 798 10 632 .765 11 602 735 12 576 .708 13 553 684 14 .532 661 15 514 641 16 497 623 17 482 606 18 468 590 19 456 575 20 .444 .561 25 396 505 30 361 463 35 335 430 40 312 402 45 294 .378 50 279 361 60 254 330 70 236 305 80 220 286 90 .207 .269 100 196 256 NOTE: To test Ho: p = 0 against Hip # 0, reject Ho if the absolute value of r is greater than the critical value in the table.12. Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) X 10 8 13 9 11 9.14 8.15 14 8.73 6 4 8.77 9.25 12 7 8.09 5.14 5 3.09 9.13 .26 4.73 5 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. O A. O B. O c. 10- Ay OD. 10- Ay 10- 8- 10 My 8 8-7 6- X 12 16 16 of X 12 16 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= (Round to three decimal places as needed. Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. O A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. O B. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. O C. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is insufficient evidence to support the claim of a linear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below. O A. The scatterplot reveals a distinct pattern that is not a straight-line pattern. O B. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. O C. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. O D. The scatterplot does not reveal a distinct pattern.5: Table of Critical Values n a = .05 a = .01 .950 990 OUI A 878 959 .811 917 .754 875 707 834 666 .798 632 .765 602 .735 576 708 .553 .684 532 661 15 514 641 16 497 623 17 482 606 18 468 590 19 456 .575 20 444 561 25 .396 505 30 361 463 35 335 430 40 312 402 45 294 378 50 279 361 60 254 330 70 236 .305 80 220 286 90 207 .269 100 196 256 NOTE: To test Hop = 0 against Hip # O, reject Ho if the absolute value of r is greater than the critical value in the table.13. Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Dete whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.05. Print Internet Users 80.5 78.7 57.1 68.2 77.6 38.2 0 Award Winners 5.7 9.2 3.4 1.7 10.4 0.1 Construct a scatterplot. Choose the correct graph below. O A. O B. O c. OD. 127 121 12 12 I Award Winners Award Winners Award Winners Award Winners OHHH 30 30 30 or 30 Internet Users Internet Users Internet Users Internet Users The linear correlation coefficient is r = (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: P (1) H1 : P ( 2 ) (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.) Because the P-value of the linear correlation coefficient is (3) the significance level, there (4) sufficient evidence to support the claim that there is a linear correlation between Internet users and scientific award winners. > (3) O greater than (4) O is O less than or equal to O is not OOOO OOOO I1 A #14. Using the weights (lb) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying data set, one gets this regression equation: y = 58.9 - 0.00749x, where x represents weight. Complete parts (a) through (d). 6 Click the icon to view the car data. a. What does the symbol y represent? O A. y represents the actual value of highway fuel consumption. O B. y represents the actual value of weight. O C. y represents the predicted value of highway fuel consumption. O D. y represents the predicted value of weight. b. What are the specific values of the slope and y-intercept of the regression line? O A. The slope is - 0.00749 and the y-intercept is 58.9. O B. The slope is 58.9 and the y-intercept is - 0.00749. O C. The slope is 58.9 and the y-intercept is 0.007499. O D. The slope is 0.00749 and the y-intercept is 58.9. c. What is the predictor variable? O A. The predictor variable is weight, which is represented by x. O B. The predictor variable is highway fuel consumption, which is represented by y. O C. The predictor variable is highway fuel consumption, which is represented by x. O D. The predictor variable is weight, which is represented by y. d. Assuming that there is a significant linear correlation between weight and highway fuel consumption, what is the best predicted value for a car that weighs 3002 lb? The best predicted value of highway fuel consumption of a car that weighs 3002 lb is mi/gal. (Round to one decimal place as needed.)