10.5

Date: 07/18/22 Course: Math 12 Summer 2022 46544 10. Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3%. A mutual-fund rating agency andomly selects 21 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.11%. Is there sufficient evidence to conclude that the fund has moderate risk at the o = 0.01 level of significance? A normal probability plot indicates that the monthly rates of eturn are normally distributed. Click the icon to view the table of critical values of the chi-square distribution. What are the correct hypotheses for this test? The null hypothesis is Ho: (1) (2) (3) The alternative hypothesis is H1: (4) (5) (6) Calculate the value of the test statistic. XO= (Round to two decimal places as needed.) Identify the critical value(s) for this test. Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the correct conclusion at the a = 0.01 level of significance? Since the test statistic is (7) than the critical value, (8) the null hypothesis. There (9) sufficient evidence at the " = 0.01 level of significance to conclude that the fund has moderate risk. 1: Chi-Square Distribution Critical Value Table Chi-Square (x ) Distribution Degrees of Area to the Right of Critical Value Freed on 0.995 0.99 0.975 0.95 0.90 OTO 0.05 0.025 0.01 0.005 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7879 0.010 0.020 0.061 0.103 0.211 4.605 5 991 7.378 9.210 10.597 0.072 0115 0.216 0.352 0.58 6.251 7815 9.348 11.345 12.838 0.207 0297 0.484 0.71 1.064 7.779 9488 11.143 13.277 14.860 141 0554 0.831 1.145 1 610 9.236 11.070 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.20 10.64 12592 14.449 16.812 18.548 0.989 1.239 1.690 2.167 2.83 12.017 14.067 16.013 18.475 20278 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17535 20.090 21.955 1.735 2.088 2.70 0 3.32 4.168 14.684 16.919 19.023 21.666 23.589 2156 2.558 3.247 3940 4 865 15.987 18.307 20.483 23 209 25.188 2603 3.053 3.816 1.575 5.57 7275 19.675 21.920 24.725 26.757 3074 3.571 4.404 5.226 6 304 18.549 21.026 23.3.37 26 217 28.300 3565 4 107 5.009 5.89 7042 19.812 24.736 27688 29.819 4075 4.660 5.629 6.571 7790 21.064 23.685 26.119 29 141 31.319 4.601 5 229 5.26 1.261 8.54 2.307 24.996 27.488 30 578 32.801 5.142 5.812 6.908 7962 9.312 23542 26.296 28.845 32000 34.267 5.697 5.408 7564 10.085 4.769 27587 30.191 $3.409 35.718 6.265 7015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37156 6.844 7633 3.907 10.117 11.651 30.144 32.852 36.19 38.582 7434 8.260 9 591 10.851 12.443 28.412 31.410 34.170 37566 39.997 8.034 8.897 10.283 11.591 13.240 29.61 32.671 35.479 38.932 41.401 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796 9.260 10.196 11.68 13.091 4.848 2.007 35.172 38.076 41.638 44.18 9.886 10 856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 15.559 10.520 1.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 16.928 11.160 12.198 13.844 15.379 17292 35.563 38 885 41.923 15.642 48.290 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49 645 12461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50993 13.121 14.256 16.04 17.708 9.768 39.087 42.557 45.722 19.588 $2336 13.787 4.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672 20.707 22.164 24.433 26.50 29.051 51.805 55.758 59 347 63691 66.766 27991 29.707 32.357 34.764 37689 63.167 67505 71,420 76.154 79 490 35 534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952 43 275 45.442 48.758 51.735 55.329 85.527 90.531 95.023 100.425 104 215 $1.172 53.540 57153 60.391 4.278 96.578 101.879 106.629 112.329 116.321 59196 61.75 65.64 69.126 73.291 107.565 113.145 118.136 124116 128.299 100 67328 70 055 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 Xi- The area to the i- - The area to the right right of this right of this of this value isa value is a. value is 1-x. The area to the right of this value is 1 - . (1) 0 (2) 0 = (3) 0 0.0211. (4) (5) 0 2 (6) 0 0.03. (7) O less (8) O do not reject 0.03. p O 0.0211. O greater O reject p OH O