Question
Asked Nov 21, 2019
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Consider the following hypothesis from a sample of 13 observations that has the value t = 2.78:
3.
Ho:u 40
Haiu40
What are the degrees of freedom for this statistic?
a.
Give the two critical values t* from t Distribution table that bracket t
b.
Between what two values does the P-value of the test fall?
c.
Is the value t 2.78 statistically significant at the 5% level? At the 1% level?
d.
Use Stata to find the exact P-value. What is the Stata command you used to find the exact P
e.
value?
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Consider the following hypothesis from a sample of 13 observations that has the value t = 2.78: 3. Ho:u 40 Haiu40 What are the degrees of freedom for this statistic? a. Give the two critical values t* from t Distribution table that bracket t b. Between what two values does the P-value of the test fall? c. Is the value t 2.78 statistically significant at the 5% level? At the 1% level? d. Use Stata to find the exact P-value. What is the Stata command you used to find the exact P e. value?

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Step 1

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Step 2

a) The degrees of freedom for t-test is n-1. Here, the sample size is 13. Therefore, the degrees of freedom is 12 (=13-1)

b) The critical value can be obtained from t table...

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cum. prob one-tail two-tails df tws ts0 tso tas 0.15 tso 0.10 tss 0.05 tss tm 0.001 0.0005 0.002 0.001 tss 0.25 0.025 0.50 0.20 0.01 0.005 0.10 1.00 0.50 0.40 0.30 0.20 0.05 0.02 0.01 3.078 1.886 0.000 1.000 1.376 1.963 6.314 12.71 31.82 63.66 318.31 636.62 1 1.06 0.978 0.941 6.965 4.541 0.000 0.816 0.765 1.386 2.920 2.353 4.303 3.182 9.925 22.327 31.599 3 4 10.215 0.000 1.250 1.638 5.841 12.924 0.741 2.132 2.776 8.610 0.000 0.000 0.000 1.190 1.156 1.533 1.476 1.440 3.747 4.604 7.173 5.893 5.208 2.015 1.943 2.571 2.447 4.032 0.727 0.920 3.365 6.869 0.906 0.896 5.959 5.408 1.134 1.119 3.707 3.499 0.718 3.143 7 0.000 0.711 1.895 2.365 2.998 4.785 1.415 1.860 1.833 2.306 4.501 0.000 0.706 0.889 1.108 1.397 2.896 3.355 5.041 0.000 0.703 0.700 0.697 0.883 1.100 1.383 2.262 2.821 3.250 4.297 4.781 10 1.812 1.796 1.782 0.000 0.000 0.879 0.876 0.873 1.093 1.088 1.372 2.228 2.201 2.764 2.718 3.169 3.106 3.055 4.144 4.587 4.437 4.318 1.363 4.025 3.930 12 13 0.000 0.695 1.083 1.356 1.350 2.179 2.681 0.000 0.000 2.160 2.145 4.221 0.694 0.870 0.868 1.079 1.771 2.650 3.012 2.977 3.852 3.787 0.692 1.076 1.761 4.140 14 1.345 1.341 1.337 2.624 15 16 17 18 19 0.000 0.000 0.691 0.690 0.866 1.074 1.071 1.753 1.746 2.131 2.120 2.602 2.583 2.947 2.921 3.733 3.686 4.073 0.865 0.863 4.015 3.965 0.000 0.000 0.689 1.069 1.333 1.740 2110 2.567 2.898 3.646 3.922 3.883 3.850 3.819 0.688 0.862 1.067 1.330 1.328 1.734 2.101 2.552 2.878 3.610 3.579 0.861 0.860 0.859 0.858 1.066 1.064 1.063 2.861 0.000 0688 1.729 2.093 2.539 0.687 0.686 0.000 0.000 0.000 0.000 2.086 2.528 2.518 2.508 20 1.325 1.323 1.321 1.725 2.845 3.552 3.527 2.831 2.819 21 1.721 2.080 2.074 22 23 24 1.061 1.060 0.686 1.717 3.505 3.792 0.858 1.319 2.069 2.500 2.807 3.485 3.768 0.685 1.714 1.059 0.685 0.857 1.318 1.711 2.064 2.492 2.797 3.467 3.450 3.435 3.745 0.000 25 26 1.316 1.315 0.000 0.684 0.684 0.856 0.856 1.058 1.058 1.708 1.706 2.060 2.056 2.485 2.479 2.787 2.779 3.725 3.707 0.000 27 28 1.057 1.703 0.000 0.684 0.855 1.314 2.052 2.473 2771 3.421 3.690 0.000 0.683 0.855 1.056 1.313 1.701 1.699 2.048 2.467 2.763 3.408 3.674 0.854 0.854 0.851 3.659 29 0.000 0.683 1.055 1.311 2.045 2.462 2.756 3.396 30 40 60 80 100 1000 1.697 1.684 2.457 2.423 2.750 3.646 3.551 3.460 0.000 0.683 1.055 1.050 1.045 1.310 1.303 1.296 2.042 3.385 2.704 2.660 0.000 0.681 2.021 3.307 0.000 1.671 2.390 3.232 0.679 0.848 2.000 0.000 0.678 0.846 0.845 1.043 1.292 1.664 1.990 2.639 3.195 2.374 3.416 3.390 0.000 0.677 1.042 1.290 1.660 1.984 2.364 2.626 3.174 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581 3.098 3.300 0.674 0.842 1.282 1.645 1.960 2.576 3.090 3.291 0.000 1.036 2.326 60% 80% 95% 0% 50% 70% 90% 99.8% 99.9% 98% 99% Confidence Level N

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