The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the data? Use a = 0.01. Hours , x 0 1 2 4 4 5 5 6 7 8, 2 Test score, y 41 42 50 49 65 69 71 78 84 97 Click here to view a table of critical values for Student's t-distribution. - X Setup the hypothesis for the test. Data table Ho: P Vo Ha: P Vo Level of Identify the critical value(s). Select the correct choice below confidence, c 0.50 0.80 0.90 0.95 0.98 0.99 (Round to three decimal places as needed.) One tail, o 0.25 0.10 0.05 0.025 0.01 0.005 d.f. Two tails, a 0.50 0.20 0.10 0.05 0.02 0.01 O A. The critical value is 1.000 3.078 6.314 12.706 31.821 63.657 O B. The critical values are - to = and to = 0.816 1.886 2.920 4.303 6.965 9.925 JAWN 0.765 1.638 2.353 3.182 4.541 5.841 0.741 1.533 2.132 2.776 3.747 4.604 Calculate the test statistic. 0.727 1.476 2.015 2.571 3.365 4.032 6 0.718 1.440 1.943 2.447 3.143 3.707 7 0.711 1.415 1.895 2.365 2.998 3.499 8 0.706 1.397 1.860 2.306 2.896 3.355 Calculate the test statistic. t=(Round to three decimal places as needed.) What is your conclusion? There enough evidence at the 1% level of significance to conclude that there a significant linear correlation between hours spent studying and test score. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x 772 628 518 508 496 483 (a) x = 502 feet (b) x = 646 feet Stories, y 51 48 46 42 38 37 (c) x = 310 feet d) x = 736 feet Find the regression equation. y = x + (D (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. OA. O B. O C. OD. 60- 60 60 Stories Stories Stories Stories 800 800 800 800 Height ( feet) Height (feet) Height ( feet) Height ( feet) (a) Predict the value of y for x = 502. Choose the correct answer below. (b) Predict the value of y for x = 646. Choose the correct answer below O A. 41 O A. 47 O B. 51 O B. 33 O C. 41 O C. 47 O D. not meaningful O D. not meaningful (c) Predict the value of y for x = 310. Choose the correct answer below. O A. 47 O B. 33 O C. 51 O D. not meaningful (d) Predict the value of y for x = 736. Choose the correct answer below. O A. 51 OB. 41 O C. 33 O D. not meaningful
