正態(tài)總體均值與方差的區(qū)間估計(jì)演示文稿

正態(tài)總體均值與方差的區(qū)間估計(jì)演示文稿當(dāng)前第1頁\共有50頁\編于星期五\2點(diǎn)（優(yōu)選）第五節(jié)正態(tài)總體均值與方差的區(qū)間估計(jì)當(dāng)前第2頁\共有50頁\編于星期五\2點(diǎn)解：滾珠平均直徑的置信水平為1-的一個(gè)置信區(qū)間為：當(dāng)前第3頁\共有50頁\編于星期五\2點(diǎn)包糖機(jī)某日開工包了12包糖,稱得質(zhì)量(單位:克)分別為506,500,495,488,504,486,505,513,521,520,512,485.假設(shè)重量服從正態(tài)分布,解附表2-1例2當(dāng)前第4頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第5頁\共有50頁\編于星期五\2點(diǎn)附表2-2查表得當(dāng)前第6頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第7頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第8頁\共有50頁\編于星期五\2點(diǎn)推導(dǎo)過程如下:當(dāng)前第9頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第10頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第11頁\共有50頁\編于星期五\2點(diǎn)解有一大批糖果,現(xiàn)從中隨機(jī)地取16袋,稱得重量(克)如下:設(shè)袋裝糖果的重量服從正態(tài)分布,試求總體均值附表3-1例2當(dāng)前第12頁\共有50頁\編于星期五\2點(diǎn)就是說估計(jì)袋裝糖果重量的均值在500.4克與507.1克之間,這個(gè)估計(jì)的可信程度為95%.這個(gè)誤差的可信度為95%.當(dāng)前第13頁\共有50頁\編于星期五\2點(diǎn)解附表3-2例3(續(xù)例1)如果只假設(shè)糖包的重量服從正態(tài)分布包糖機(jī)某日開工包了12包糖,稱得質(zhì)量(單位:克)分別為506,500,495,488,504,486,505,513,521,520,512,485.當(dāng)前第14頁\共有50頁\編于星期五\2點(diǎn)解例4當(dāng)前第15頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第16頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第17頁\共有50頁\編于星期五\2點(diǎn)推導(dǎo)過程如下:根據(jù)第六章第二節(jié)定理二知2.當(dāng)前第18頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第19頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第20頁\共有50頁\編于星期五\2點(diǎn)進(jìn)一步可得:注意:在密度函數(shù)不對(duì)稱時(shí),習(xí)慣上仍取對(duì)稱的分位點(diǎn)來確定置信區(qū)間(如圖).當(dāng)前第21頁\共有50頁\編于星期五\2點(diǎn)解有一大批糖果,現(xiàn)從中隨機(jī)地取16袋,稱得重量(克)如下:設(shè)袋裝糖果的重量服從正態(tài)分布,試求總體標(biāo)準(zhǔn)差

的置信水平為0.95的置信區(qū)間例5代入公式得標(biāo)準(zhǔn)差的置信區(qū)間附表4-1附表4-2當(dāng)前第22頁\共有50頁\編于星期五\2點(diǎn)從某廠生產(chǎn)的滾珠中隨機(jī)抽取10個(gè)，測(cè)得滾珠的直徑(單位mm)如下：14.6,15.0,14.7,15.1,14.9,14.8,15.0,15.1,15.2,14.8。若滾珠直徑服從正態(tài)當(dāng)前第23頁\共有50頁\編于星期五\2點(diǎn)二、兩個(gè)總體的情況討論兩個(gè)整體總體均值差和方差比的估計(jì)問題.當(dāng)前第24頁\共有50頁\編于星期五\2點(diǎn)推導(dǎo)過程如下:1.當(dāng)前第25頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第26頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第27頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第28頁\共有50頁\編于星期五\2點(diǎn)例7為比較?,??兩種型號(hào)步槍子彈的槍口速度,隨機(jī)地取?型子彈10發(fā),得到槍口速度的平均值為隨機(jī)地取??型子彈20發(fā),得槍口速度平均值為假設(shè)兩總體都可認(rèn)為近似地服從正態(tài)分布,且由生產(chǎn)過程可認(rèn)為它們的方差相等,求兩總體均值差信區(qū)間.解由題意,兩總體樣本獨(dú)立且方差相等(但未知),當(dāng)前第29頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第30頁\共有50頁\編于星期五\2點(diǎn)解由題意,兩總體樣本獨(dú)立且方差相等(但未知),例8為提高某一化學(xué)生產(chǎn)過程的得率,試圖采用一種新的催化劑,為慎重起見,在試驗(yàn)工廠先進(jìn)行體都可認(rèn)為近似地服從正態(tài)分布,且方差相等,求兩總體均值差試驗(yàn).設(shè)采用原來的催化劑進(jìn)行了次試驗(yàn),得到得率的平均值又采用新的催化劑進(jìn)行了次試驗(yàn),得到得率的平均值假設(shè)兩總當(dāng)前第31頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第32頁\共有50頁\編于星期五\2點(diǎn)解：當(dāng)前第33頁\共有50頁\編于星期五\2點(diǎn)liti9當(dāng)前第34頁\共有50頁\編于星期五\2點(diǎn)推導(dǎo)過程如下:2.當(dāng)前第35頁\共有50頁\編于星期五\2點(diǎn)根據(jù)F分布的定義,知當(dāng)前第36頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第37頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第38頁\共有50頁\編于星期五\2點(diǎn)解例9研究由機(jī)器A和機(jī)器B生產(chǎn)的鋼管內(nèi)徑,隨機(jī)抽取機(jī)器A生產(chǎn)的管子18只,測(cè)得樣本方差為均未知,求方差比區(qū)間.設(shè)兩樣本相互獨(dú)抽取機(jī)器B生產(chǎn)的管子13只,測(cè)得樣本方差為立,且設(shè)由機(jī)器A和機(jī)器B生產(chǎn)的鋼管內(nèi)徑分別服從正態(tài)分布信當(dāng)前第39頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第40頁\共有50頁\編于星期五\2點(diǎn)解例10甲、乙兩臺(tái)機(jī)床加工同一種零件,在機(jī)床甲加工的零件中抽取9個(gè)樣品,在機(jī)床乙加工的零件信區(qū)間.假定測(cè)量值都服從正態(tài)分布,方差分別為的置在置信度由所給數(shù)據(jù)算得0.98下,試求這兩臺(tái)機(jī)床加工精度之比中抽取6個(gè)樣品,并分別測(cè)得它們的長度(單位:mm),當(dāng)前第41頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第42頁\共有50頁\編于星期五\2點(diǎn)三、小結(jié)當(dāng)前第43頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第44頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第45頁\共有50頁\編于星期五\2點(diǎn)本章作業(yè)第173-176頁（1）點(diǎn)估計(jì)第2、3、4、8、11、15題、（2）區(qū)間估計(jì)16題、18題、19題、21題、22題、23題、25題當(dāng)前第46頁\共有50頁\編于星期五\2點(diǎn)附表2-1標(biāo)準(zhǔn)正態(tài)分布表z01234567890.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.65540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.51200.55170.59100.62930.66640.70190.73570.76730.79670.82380.84850.87080.89070.90820.92360.93700.94840.51600.55570.59480.63310.67000.70540.73890.77030.79950.82640.85080.87290.89250.90990.92510.93820.94950.51990.55960.59870.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645當(dāng)前第47頁\共有50頁\編于星期五\2點(diǎn)當(dāng)前第48頁\共有50頁\編于星期五\2點(diǎn)附表3-1=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812