申論 4某縣市衛生局欲評估某降低血壓（符合常態分佈）之健康促進計畫（X=1，介入；X=0，無介入），研究者共邀請20 位民眾參與計畫，並測量其前後血壓值之改變。依資料產生下列結果回答以下子題㈠及子題㈡：介入前平均分數及標準差：Y (標準差, SD) = 136.6 (18.58)介入後平均分數及標準差：Y (標準差, SD) = 129.9 (14.94)d =–6.7∑k(d−d)2=2486－－－－－－－－－－－－－－－－－(1)i=1i㈠回答下列問題：（4 分）回答上述式(1)之k 值。計算前後差異值（d）之標準差（SD）。d㈡若上述結果以雙尾檢定檢視介入前後平均血壓是否有差別，請回答下列問題：（每小題3 分，共15 分）以前述符號設立虛無及對立假說。介入前後差異平均值之變異數（Var( d )）大小。依上述結果及在虛無假說下進行檢定，其檢定統計值大小及其自由度。計算介入前後差異平均值之95%信賴區間。以題判斷是否拒絕虛無假說。㈢若將上述前後測結果重覆500 次，請回答下列問題：（每小題3 分，共6 分）此500 次樣本平均值之分佈接近何種分佈？上述題在虛無假說下之平均值及變異數。（如果原母群體前後差異之變異數（σ 2）為144）d㈣若將上述前後介入視為兩組獨立樣本以簡單線性迴歸分析得到如下結果，⎧1介入後yˆ=αˆ+βˆx 其中yˆ ：血壓值, x (組別) = ⎨⎩0介入前請回答下列問題。（每小題5 分，共25 分）利用前面介入前後所提供之平均值結果，計算αˆ 及βˆ 。利用前面所提供介入前後之標準差計算βˆ 之標準誤。若使用兩組獨立樣本t 檢定，計算t 值。若使用一方變異數分析（One-way ANOVA）進行檢定，敍述所用檢定統計值及大小。此題分析方法相較於前面題的最大缺點是未考慮統計上的何種特性？標準常態分佈表 卡方分佈表右尾機率z 右尾 z 右尾 z 右尾 z 右尾 z 右尾z 右尾機率 機率 機率 機率 機率機率d.f.0.0250.20.15 0.1 0.050.0250.005t 分佈表 F 分佈表雙尾機率 分母右尾分子自由度自由度機率右尾 12351038 39 40 787980機率 10.1 39.86 49.50 53.59 57.24 60.19 62.49 62.51 62.53 62.92 62.9262.93d.f. 0.25 0.2 0.15 0.1 0.050.025 0.005 0.05 161.4 199.5 215.7 230.1 241.8 250.9 251.0 251.1 252.6 252.7 252.721 1.0000 1.3764 1.9626 3.0777 6.3138 12.7062 63.6567 0.025 647.7 799.5 864.1 921.8 968.6 1004. 1005. 1005. 1011. 1011. 1011.92 0.8165 1.0607 1.3862 1.8856 2.92004.3027 9.9248 20.18.539.009.169.299.399.46 9.47 9.47 9.489.489.483 0.7649 0.9785 1.2498 1.6377 2.35343.1824 5.8409 0.05 18.51 19.00 19.16 19.30 19.40 19.47 19.47 19.47 19.48 19.4819.484 0.7407 0.9410 1.1896 1.5332 2.13182.7764 4.6041 0.025 38.51 39.00 39.17 39.30 39.40 39.47 39.47 39.47 39.49 39.4939.495 0.7267 0.9195 1.1558 1.4759 2.01502.5706 4.0321 30.15.545.465.395.315.235.16 5.16 5.16 5.155.155.156 0.7176 0.9057 1.1342 1.4398 1.94322.4469 3.7074 0.05 10.139.559.289.018.798.60 8.60 8.59 8.568.568.567 0.7111 0.8960 1.1192 1.4149 1.89462.3646 3.4995 0.025 17.44 16.04 15.44 14.88 14.42 14.04 14.04 14.04 13.97 13.9713.978 0.7064 0.8889 1.1081 1.3968 1.85952.3060 3.35549 0.7027 0.8834 1.0997 1.3830 1.83312.2622 3.2498 0.056.615.795.415.054.744.47 4.47 4.46 4.424.424.4110 0.6998 0.8791 1.0931 1.3722 1.81252.2281 3.1693 0.025 10.018.437.767.156.626.18 6.18 6.18 6.106.106.1011 0.6974 0.8755 1.0877 1.3634 1.79592.2010 3.105812 0.6955 0.8726 1.0832 1.3562 1.78232.1788 3.0545 0.054.964.103.713.332.982.67 2.66 2.66 2.602.602.6013 0.6938 0.8702 1.0795 1.3502 1.77092.1604 3.0123 0.0256.945.464.834.243.723.26 3.26 3.26 3.173.173.1714 0.6924 0.8681 1.0763 1.3450 1.76132.1448 2.976815 0.6912 0.8662 1.0735 1.3406 1.75312.1314 2.9467 380.12.842.452.232.011.771.52 1.52 1.52 1.461.461.4616 0.6901 0.8647 1.0711 1.3368 1.74592.1199 2.9208 0.0255.454.073.482.922.411.91 1.90 1.90 1.791.791.7917 0.6892 0.8633 1.0690 1.3334 1.73962.1098 2.898218 0.6884 0.8620 1.0672 1.3304 1.73412.1009 2.8784 390.12.842.442.232.001.771.52 1.51 1.51 1.451.451.4519 0.6876 0.8610 1.0655 1.3277 1.72912.0930 2.8609 0.054.093.242.852.462.081.71 1.70 1.70 1.621.621.6220 0.6870 0.8600 1.0640 1.3253 1.72472.0860 2.845321 0.6864 0.8591 1.0627 1.3232 1.72072.0796 2.8314 400.12.842.442.232.001.761.51 1.51 1.51 1.451.451.4522 0.6858 0.8583 1.0614 1.3212 1.71712.0739 2.8188 0.054.083.232.842.452.081.70 1.70 1.69 1.611.611.6123 0.6853 0.8575 1.0603 1.3195 1.71392.0687 2.807324 0.6848 0.8569 1.0593 1.3178 1.71092.0639 2.7969 780.12.772.372.161.921.681.41 1.41 1.41 1.341.341.3425 0.6844 0.8562 1.0584 1.3163 1.70812.0595 2.7874 0.053.963.112.722.331.951.56 1.55 1.55 1.451.451.4526 0.6840 0.8557 1.0575 1.3150 1.70562.0555 2.7787 0.0255.223.873.292.732.221.70 1.69 1.68 1.561.561.5627 0.6837 0.8551 1.0567 1.3137 1.70332.0518 2.7707 790.12.772.372.151.921.681.41 1.41 1.40 1.341.341.3428 0.6834 0.8546 1.0560 1.3125 1.70112.0484 2.7633 0.053.963.112.722.331.951.56 1.55 1.55 1.451.451.4529 0.6830 0.8542 1.0553 1.3114 1.69912.0452 2.7564 0.0255.223.873.292.732.221.69 1.69 1.68 1.561.561.5630 0.6828 0.8538 1.0547 1.3104 1.69732.0423 2.7500 800.12.772.372.151.921.681.41 1.41 1.40 1.341.331.3331 0.6825 0.8534 1.0541 1.3095 1.69552.0395 2.7440 0.053.963.112.722.331.951.55 1.55 1.54 1.451.451.4532 0.6822 0.8530 1.0535 1.3086 1.69392.0369 2.7385 0.0255.223.863.282.732.211.69 1.68 1.68 1.561.561.5533 0.6820 0.8526 1.0530 1.3077 1.69242.0345 2.733334 0.6818 0.8523 1.0525 1.3070 1.69092.0322 2.728435 0.6816 0.8520 1.0520 1.3062 1.68962.0301 2.723836 0.6814 0.8517 1.0516 1.3055 1.68832.0281 2.719537 0.6812 0.8514 1.0512 1.3049 1.68712.0262 2.715438 0.6810 0.8512 1.0508 1.3042 1.68602.0244 2.711639 0.6808 0.8509 1.0504 1.3036 1.68492.0227 2.707940 0.6807 0.8507 1.0500 1.3031 1.68392.0211 2.704576 0.6777 0.8464 1.0436 1.2928 1.66521.9917 2.642177 0.6777 0.8463 1.0435 1.2926 1.66491.9913 2.641278 0.6776 0.8463 1.0434 1.2925 1.66461.9908 2.640379 0.6776 0.8462 1.0433 1.2924 1.66441.9905 2.639580 0.6776 0.8461 1.0432 1.2922 1.66411.9901 2.6387∞ 0.6745 0.8416 1.0364 1.2816 1.64491.9600 2.5758