Question

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Suppose that a sample of 20 pairs of data produced a test statistic of r = 0.515. A significance level of a = 0.05 is to be used. (a) Find the critical values that would be used to test for significant linear correlation. Do not type "+" in front of your answer (the is already given in front of the answer box below). Round your answer to 3 places after the decimal point, if necessary. 0.9- (b) Is there significant linear correlation in this case? There is not significant linear correlation. There is significant linear correlation.

Answer 1

9 We have : n = 20 8= 0.515 Q = 0.05. We are testing Ho : p=0 versus He : P to The test Statistic is t run-2 0.515 20-2 2.549 V1-82 Not-0.5152 Critical Value: tig @ 2.5% = 2.101 (two-tailed) since, 2.101 < 2.549 we have sufficient Evidence to Reject the Hull hypothesis at 5% significance level. Hence, we conclude that There is significant linear correlation. the

Percentage Points for the t distribution This table gives percentage points x defined by the equation 00 dt P= 1 1(12v+2) TvT (12v) X (1+2+/)%*) Р 0 х The limiting distribution of t as v tends to infinity is the standard normal distribution. When v is large, interpolation in v should be harmonic. P= 40% 30% 25% 20% 15% 10% 5% 2.5% 1% 0.5% 0.1% 0.05% V 1 0.3249 0.7265 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.3 636.6 2 0.2887 0.6172 0.8165 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.33 31.60 3 0.2767 0.5844 0.7649 0.9785 1.250 1.638 2.353 3.182 4.541 5.841 10.21 12.92 4 0.2707 0.5686 0.7407 0.9410 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.2672 0.5594 0.7267 0.9195 1.156 1.476 2.015 2.571 3.365 4.032 5.894 6.869 6 0.2648 0.5534 0.7176 0.9057 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.2632 0.5491 0.7111 0.8960 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.2619 0.5459 0.7064 0.8889 1.108 1.397 1.860 - 2.306 - 2.896 3.355 4.501 5.041 9 0.2610 0.5435 0.7027 0.8834 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.2602 0.5415 0.6998 0.8791 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.2596 0.5399 0.6974 0.8755 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.2590 0.5386 0.6955 0.8726 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.2586 0.5375 0.6938 0.8702 1.079 1.350 1.771 2.160 2.650 3.0123.852 4.221 14 0.2582 0.5366 0.6924 0.8681 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 0.2579 0.5357 0.6912 0.8662 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 0.2576 0.5356 0.6901 0.8647 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 0.2573 0.5344 0.6892 0.8633 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 0.2571 0.5338 0.6884 0.8620 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.2569 0.5333 0.6876 0.8610 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.2567 0.5329 0.6870 0.8600 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.2566 0.5325 0.6864 0.8591 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.2564 0.5321 0.6858 0.8583 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 0.2563 0.5317 0.6853 0.8575 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768 24 0.2562 0.5314 0.6848 0.8569 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 0.2561 0.5312 0.6844 0.8562 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 0.2560 0.5309 0.6840 0.8557 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 0.2559 0.5306 0.6837 0.8551 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.689 28 0.2558 0.5304 0.6834 0.8546 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.2557 0.5302 0.6830 0.8542 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.660 30 0.2556 0.5300 0.6828 0.8538 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 32 0.2555 0.5297 0.6822 0.8530 1.054 1.309 1.694 2.037 2.449 2.738 3.365 3.622- 34 0.2553 0.5294 0.6818 0.8523 1.052 1.307 1.691 2.032 2.441 2.728 3.348 3.601 36 0.2552 0.5291 0.6814 0.8517 1.052 1.306 1.688 2.028 2.434 2.719 3.333 3.582 38 0.2551 0.5288 0.6810 0.8512 1.051 1.304 1.686 2.024 2.429 2.712 3.319 3.566 40 0.2550 0.5286 0.6807 0.8507 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551 50 0.2547 0.5278 0.6794 0.8489 1.047 1.299 1.676 2.009 2.403 2.678 3.261 3.496 60 0.2545 0.5272 0.6786 0.8477 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460 120 0.2539 0.5258 0.6765 0.8446 1.041 1.289 1.658 1.980 2.358 2.617 3.160 3.373 0.2533 0.5244 0.6745 0.8416 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291