Answer Happy

Data Table Age, x 1 2 3 Vocabulary size, y 6 250 540 1100 2100 2600 4 5 6 3 590 5 2 4 2400 240 1200 2500 6

Critical Values for the Pearson Correlation coefficient o Critical Values for the Pearson Correlation Coefficient The correlation is significant when the absolute value of 1 is greater than the value in the table. n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 a = 0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 Q = 0.01 0.990 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 AROR 102

Critical Values for the Pearson Correlation coefficient 17 18 19 20 21 22 23 24 25 26 27 28 29 30 35 0.482 0.468 0.456 0.444 0.433 0.423 0.413 0.404 0.396 0.388 0.381 0.374 0.367 0.361 0.334 0.312 0.294 0.279 0.266 0.254 0.244 0.235 0.227 0.220 0.606 0.590 0.575 0.561 0.549 0.537 0.526 0.515 0.505 0.496 0.487 0.479 0.471 0.463 0.430 0.403 0.380 0.361 0.345 0.330 0.317 0.306 0.296 0.286 40 45 50 55 60 65 70 75 80

Values for the Pearson Correlation Coefficient 23 24 25 26 27 28 29 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 n 0.413 0.404 0.396 0.388 0.381 0.374 0.367 0.361 0.334 0.312 0.294 0.279 0.266 0.254 0.244 0.235 0.227 0.220 0.213 0.207 0.202 0.197 a = 0.05 0.526 0.515 0.505 0.496 0.487 0.479 0.471 0.463 0.430 0.403 0.380 0.361 0.345 0.330 0.317 0.306 0.296 0.286 0.278 0.270 0.263 0.256 a = 0.01

The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Completo parts (a) through (d) below. Click here to view the data table. Click here to view the table of critical values for the Pearson correlation coefficient CHOD (a) Display the data in a scatter plot. Choose the correct graph below. ОА Ов, Q OC OD 8 0 6 Vocabulary size oo 4 Vocabulary size 3000 2400 1800 1200 500 0-4 0 2 4 6 8 Age (years) Vocabulary 2 3000 2400 1800 1200 600 0 0 2 4 Age (years) Vocabulary 2+ 0 0 1500 3000 Age (years) 3000 1500 Age years (b) Calculate the sample correlation coefficient r. (Round to three decimal places as needed.) (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. linear correlation Interpret the correlation. Choose the correct answer below. There is

The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Complete parts (a) through (d) below. Click here to view the data table Click here to view the table of critical values for the Pearson correlation coefficient There is (Round to three decimal places as needed.) (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data, linear correlation Interpret the correlation. Choose the correct answer below. A. Aging causes the number of words in children's vocabulary to increase B. Based on the correlation, there does not appear to be a linear relationship between children's ages and the number of words in their vocabulary C. Based on the correlation, there does not appear to be any relationship between children's apes and the number of words in their vocabulary OD. As ago Increases, the number of words in children's vocabulary tends to decrease O E. Aging causes the number of words in children's vocabulary to decrease OF. As age increases, the number of words in children's vocabulary tends to increase (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let u=0.01. The critical value is Therefore, there sufficient evidence at the 1% level of significance to conclude that children's ages and the number of words in their vocabulary (Round to three decimal places as needed.) between