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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.

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Age, x Vocabulary size, y 260 550 1100 2100 2500 680 2300 270 1200 2400 4 4Critical Values for the Pearson Correlation Coefficient The correlation is significant when the absolute value of is greater than the value in the table α 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 0.482 0.468 0.456 0.444 0.433 0.423 0413 0.404 0.396 0.388 0.381 0.374 0.387 0.361 0.334 0.312 0.294 0.279 0.266 0.254 0.244 0.235 0.227 0.220 0.213 207 0.202 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 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 0.278 0.270 0.263 0.256 a0.01 10 12 13 15 16 17 18 75O A. O B. Ос. ○ D. 300 240 600 1500 3000 Age (years) 1500 3000 Age (yeara) Age (years) 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. There is Interpret the correlation. Choose the correct answer below O A. As age increases, the number of words in childrens vocabulary tends to decrease linear correlation. O B. Aging causes the number of words in childrens vocabulary to decrease C. As age increases, the number of words in childrens vocabulary tends to increase O D. Based on the correlation, there does not appear to be a linear relationship between childrens ages and the number of words in their vocabulary O E. Aging causes the number of words in childrens vocabulary to increase O F Based on the correlation, there does not appear to be any relationship between childrens ages and the number of words in their vocabulary. (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α-001. The critical value is Therefore, there ▼ (Round to three decimal places as needed.) sufficient evidence at the 1%level of significance to conclude that between childrens ages and the number of words in their vocabulary.

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Corve 0,9 44 2 o 0 00 20.9卍4 cemelati on the nianbirs VX increase sords in dulden vocabidaiy 幻 ー12,2979 I 2 oges and thu unbur werda in hi vocabulahy

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