Homework 10.5 Statistics
12. Data show that men between the ages of 20 and 29 have a mean height of 69.3 inches, with a standard deviation of 2.7 inches. A baseball analyst wonders whether the standard deviation of heights of professional baseball players is less than 2.7 inches. The heights (in inches) of 20 randomly selected players are shown in the table. The heights of men between the ages of 20 and 29 are known to be normally distributed. Complete parts (a) and (b) below. Click here to view the data table." Click here to view the chi-square distribution table. (a) Compute the sample standard deviation. inches Round to two decimal places as needed.) (b) Test the notion at the o = 0.10 level of significance. What are the correct hypotheses for this test? Ho : (1 ) . (2) versus H 1 : (3 ) (4) Type integers or decimals. Do not round.) Calculate the value of the test statistic. XO = (Round to two decimal places as needed.) Approximate the P-value for the test statistic. Choose the correct answer below. O A. The P-value is between 0.025 and 0.05. O B. The P-value is between 0.005 and 0.01. O C. The P-value is between 0.01 and 0.025. O D. The P-value is between 0.05 and 0. 10. O E. The P-value is greater than 0. 10. OF. The P-value is less than 0.005. What is the correct conclusion at the o = 0.10 level of significance? Since the P-value is (5) - than the level of significance, (6) - the null hypothesis. There (7) sufficient evidence to conclude that the standard deviation of heights of professional baseball players is (8). the standard deviation of heights of men between the ages of 20 and 29 at the 0.10 level of significance. 5: Height Data 72 74 71 71 76 70 77 76 72 72 77 73 75 70 73 74 75 73 74 74 6: Chi-Square Distribution Table Chi-Square (x2) Distribution Area to the Right of Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 0.072 0.115 0.216 0.352 0.584 7815 9.348 11.345 12.838 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1,145 1.610 9.236 11.070 12.833 5.086 16.750 0.676 0.872 1237 1.635 2.204 10.645 12.592 14.449 6.812 18.548 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 1.646 2.18 2.733 3.490 13.362 15 207 17535 20.090 21.955 1.735 2.088 2.700 3.325 4.168 14.684 6.919 19.023 21.66 23.589 2.15 2.558 3.247 3040 4.865 15.987 18.30 20.483 23.209 25.188 2.603 3.053 3.816 4 575 5.578 17275 9.675 21.920 24.725 26.757 3.074 3.571 4.404 5.226 6.304 18.549 21.02 23.337 26.217 28.300 3.56 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.68 29.819 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.1 19 29.14 31.319 4.601 5.229 6.262 7261 22.307 24.996 27488 30.578 32.801 5.142 5.812 6.908 7962 9.312 23.542 26.296 28.845 32.000 34.267 5.697 6.408 7.564 8.672 10.08 24.769 27587 30.191 33.409 35.718 6.265 7015 8.231 9.390 10.86 25.989 28.869 31.526 34.805 37.156 6.844 7633 8.907 10.117 11.651 27.204 30.144 32.852 36.19 38.582 7.434 8.260 9.591 10.851 12.44 28.41 31.410 34.170 37.566 39.997 8.034 8.897 10.283 11.591 13.240 29.615 32.67 35.479 38.932 $1,401 8.64 9.542 10.98 12.338 14.04 30813 33.924 36.781 40 289 42.796 9.26 10.196 11.689 13.091 32.007 35.172 38.076 41.638 44.181 9.88 10.856 12.401 13 848 15.65 33.196 36.415 39.364 42.980 45.559 10.520 11.524 13.120 14.611 16.473 34.382 37652 40.646 44.314 46.928 11.16 12.19 13.84 15.379 17292 35.563 38.885 41.923 45.64 48.290 11.808 12.879 14.573 16.151 18.11 36.741 40.113 43.195 46.963 49.645 12.46 13.265 15.308 16.928 18.93 37916 41.337 44.461 48.27 50.993 13.121 14.256 16.047 17.708 19.76 39.087 42.557 45.722 49.588 52.336 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.970 50.892 53.672 20.70 22.16 24.433 26.50 29.05 51.805 55.758 59.342 63.691 66.766 27.991 29.707 32.357 34.764 37.68 63.167 67505 71.420 76.154 79.490 35.534 37485 40.482 43.188 46.45 74.397 79.082 83.298 88.379 91.952 43.275 45.442 48.758 51.739 55.32 85.527 90.53 95.023 100.425 104.215 51.172 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 116.321 59.196 61.754 65.647 69.126 73.291 107565 13.145 118.136 124.116 128.299 $7.328 70.065 74.222 77929 82.358 118.498 124.342 129.561 135.807 140.169 Left tail Right tail Area - 1-a Two tails The area to the -The area to the X1-4 - The area to the right right of this right of this of this value is a value is a value is 1-a. The area to the right of this value is 1- a. (1) (3) O P (4) O = (5) O greater (6) O reject 7) O is not (8) O different from O
