SECTION 9.1 Correlation 477 To use Table 11 to test a correlation coefficient, note that the requirements for calculating a correlation coefficient given on page 473 also apply to the test. In this text, unless stated otherwise, you can assume that these requirements are met. Using Table 11 for a Correlation Coefficient In Example 5, you used 25 pairs of data to find r ≈ 0.979. Is the correlation coefficient significant? Use a = 0.05. SOLUTION The number of pairs of data is 25, so n = 25. The level of significance is a = 0.05. Using Table 11, find the critical value in the a = 0.05 column that corresponds to the row with n = 25. The number in that column and row is 0.396. a n = 0.05 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 14 0.532 = 0.01 0.990 0.959 0.917 0.875 11 0.602 0.735 13 12 0.553 0.576 0.684 0.708 0.834 0.798 0.765 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 a 19 0.456 20 0.444 0.575 0.561 21 0.433 22 0.423 23 0.413 27 28 0.381 0.374 29 0.367 0.549 0.537 0.526 0.487 0.479 0.471 24 0.404 0.396 26 0.388 0.515 0.505 0.496 n = 25 25 Critical values for = 0.05 α Because 0 r0 ≈ 0.979 7 0.396, you can decide that the population correlation is significant. Interpretation There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the duration of Old Faithful’s eruptions and the time between eruptions. TRY IT YOURSELF 6 In Try It Yourself 4, you calculated the correlation coefficient of the number of years out of school and annual contribution data to be r ≈ -0.908. Is the correlation coefficient significant? Use a = 0.01. Answer: Page A42 In Table 11, notice that for fewer data pairs (smaller values of n), stronger evidence is needed to conclude that the correlation coefficient is significant. EXAMPLE 6
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