n alpha=0.05 alpha=0.01
4 0.950 0.990
5 0.878 0.959
6 0.811 0.917
7 0.754 0.875
8 0.707 0.834
9 0.666 0.798
10 0.632 0.765
11 0.602 0.735
12 0.576 0.708
13 0.553 0.684
14 0.532 0.661
15 0.514 0.641
16 0.497 0.623
17 0.482 0.606
18 0.468 0.590
19 0.456 0.575
20 0.444 0.561
21 0.433 0.549
22 0.423 0.537
23 0.413 0.526
24 0.404 0.515
25 0.396 0.505
26 0.388 0.496
27 0.381 0.487
28 0.374 0.479
29 0.367 0.471
30 0.361 0.463
35 0.334 0.430
40 0.312 0.403
45 0.294 0.380
50 0.279 0.361
55 0.266 0.345
60 0.254 0.330
65 0.244 0.317
70 0.235 0.306
75 0.227 0.296
80 0.220 0.286
85 0.213 0.278
90 0.207 0.270
95 0.202 0.263
100 0.197 0.256
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 coeicient. (a) Display the data in a scatter plot. Choose the correct graph below. (9 A. O B. o c. a 8 to\" 3 V S S 7 . ,3 .3 e g Q S E 4 Q E . E E . . 0 _> , 0 1500 3000 0 1500 3000 Age (yearS) Age (yearS) (b) Calculate the sample correlation coefcient r, 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 7 linear correlation, Interpret the correlation. Choose the correct answer below. O A. Based on the correlation, there does not appear to be any relationship between children's ages and the number of words in their vocabulary. O B. Aging causes the number of words in children's vocabulary to decrease. O C. As age increases, the number of words in children's vocabulary tends to increase. Vocabulary size Age (years) (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is linear correlation. Interpret the correlation. Choose the correct answer below. O A. Based on the correlation, there does not appear to be any relationship between children's ages and the number of words in their vocabulary. O B. Aging causes the number of words in children's vocabulary to decrease. O C. As age increases, the number of words in children's vocabulary tends to increase. O D. As age 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 increase. OF. 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 (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let a = 0.01. The critical value is . Therefore, there V sufficient evidence at the 1% level of significance to conclude that between children's ages and the number of words in their vocabulary. (Round to three decimal places as needed.)
