• 沒有找到結果。

National Sun Yat-sen University Institutional Repository:Item 987654321/38704

N/A
N/A
Protected

Academic year: 2021

Share "National Sun Yat-sen University Institutional Repository:Item 987654321/38704"

Copied!
9
0
0

加載中.... (立即查看全文)

全文

(1)

行政院國家科學委員會補助專題研究計畫

▇ 成 果 報 告

□期中進度報告

使用空間網狀結構來拘限發光高分子之凝聚

計畫類別:

個別型計畫 □ 整合型計畫

計畫編號:NSC 96- 2221 - E - 110 -043 -

執行期間: 96 年 8 月 1 日至 97 年 7 月 31 日

計畫主持人:洪金龍

共同主持人:

計畫參與人員:

成果報告類型(依經費核定清單規定繳交):

精簡報告 □完整報告

本成果報告包括以下應繳交之附件:

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

處理方式:除產學合作研究計畫、提升產業技術及人才培育研究計畫、

列管計畫及下列情形者外,得立即公開查詢

□涉及專利或其他智慧財產權,□一年□二年後可公開查

執行單位:國立中山大學材料科學研究所

中 華 民 國 97 年 8 月 31 日

附件一

(2)

行政院國科會專題研究計畫成果報告

使用空間網狀結構來拘限發光高分子之凝聚

計畫編號:

96-2221-E-110-043

執行期限:96/08/01 ~ 97/07/31

主持人:洪金龍 教授 國立中山大學材料科學研究所

計畫參與人員: 簡榮宏 國立中山大學材料科學研究所

賴俊廷 國立中山大學材料科學研究所

一、中文摘要 螢光放光聚茀 (polyfluorenes)及其衍 生物之分子鏈照光時易於產生群聚(激發 雙體、凝聚體),導致放光效率大幅下降。 故 本 研 究 合 成 具 茀 (fluorene) 及 蔥 (anthracene)單元之交替(alternative)及團鏈 (block)共聚物,並將其植入聚甲基丙烯酸 甲酯(poly(methyl methacrylate), PMMA)交 聯網狀結構基材中,以限制聚茀之群聚, 並增進其於高溫之放光穩定度。

關鍵字:發光高分子、聚茀交替及團鏈共 聚物、群聚、激發雙体、交聯網 狀結構。

Chain segments of fluorescent polyfluorene and its derivatives tend to associate to form aggregate and excimer when excited by light. This chain association directly leads to the great reduction on the emission intensity. This research prepared alternative and block copolymers with fluorene and anthracene units. The resulting copolymers were then implanted in crosslinked poly(methyl methacrylate) (PMMA) network matrix to restrict their association and to enhance their

luminescent stability at high temperature. Keywords: Light-emitting polymer,

fluorene-based alternative and block copolymers, aggregate, excimer, crosslinked network. 二、緣由與目的 有機發光芳小分子及高分子諸如茈 (pyrene) 、 蔥 (anthracene) 、 聚 茀 (polyfluorenes)及其衍生物等具有良好紫 外 光 吸 收 (absorption) 及 螢 光 發 射 (fluorescence emission)性 [1],但此等發光 小分子及高分子於高濃度溶液態或固態時 會集結(associate),影響發光:如果其集結 態 牽 涉 激 發 態 (exciting state) 與 基 態 (ground state)的一對分子,則會產生激發 雙体(excimer)之螢光[2],如果其集結態牽 涉基態中一對以上之分子,則其激發態會 產生群聚(aggregate)螢光[3,4],激發雙体及 群聚除了會產生紅位移(red-shift)外,亦會 讓能量大量流失,造成量子效率(quantum

(3)

yield)之低落,故防止或減少激發雙体及群 聚之產生為一重大課題。 聚茀 (polyfluorenes, PF)及其衍生物 為用於有機發光二極體之高分子[5,6],其 具高效率之藍光放光、高載子(exciton)移 動率及良好加工性[7]。但聚茀薄膜亦具若 干藍至綠區基於激發雙体及群聚導致之不 純色光[8,9],此不純光造成聚茀量子效率 (quantum efficiency)之低落,故以往已有許 多研究嘗試使用化學修飾法來改進此方面 之缺失[10-12]。 本 研 究 合 成 茀 (fluorene) 及 蔥 (anthracene)單元之交替(alternative)及團鏈 (block)共聚物〈a-PFA, b-PMMA-PFA; 見 流程一及二〉,並將其植入聚甲基丙烯酸甲

酯(poly(methyl methacrylate), PMMA)交聯 網狀結構基材中,以限制聚茀之群聚,並 增進其於高溫之放光穩定度。 二、 研究方法 單體二、三及高分子PF 之合成步驟 見於流程一及二,同時文獻[13-15]已有記 載,此處不重複;而高分子 a-PFA 及 b-PMMA-PFA 之合成步驟則詳述如下: a. a-PFA〈見流程一〉

Solution of monomer 3 (1.172 g, 2 mmol), 9,10-dibromoanthracene (0.672 g, 2 mmol), Aliquat 336 (20 mg, 0.04 mmol) and

[Pd(PPh3)4] (11 mg, 0.01 mmol) in a mixture

of toluene (6 mL) and aqueous 2M K2CO3

(4 mL) was vigorously stirred at 48 h. After

the mixture was cooled to room temperature, it was poured into 200 mL of methanol. The precipitates were filtered and dried to obtain the final polymer, a-PFA. Anal. Calcd for

a-PFA: C39H40: C, 92.07; H, 7.93. Found: C,

91.79, H, 7.79. 1H NMR (CDCl3, δ(ppm)):

δ 8.65 (d, 2H, aromatic protons), δ 7.40-7.84 (m, 12H, aromatic protons), δ 2.02 (m, 4H,

-PHC(CH2CH2)2), δ 0.71-1.29 (m, 22 H,

alkyl-H) (see Figure 2.4). Mn=15500, Mw =

29600, Mw/Mn = 1.91 (GPC).

b. b-PMMA-PFA 之合成〈見流程二〉

Synthesis of PFA-OH. To the mixture of monomer 3 (2.344 g, 4 mmol), 9,10-dibromoanthracene (1.612 g, 4.4 mmol), 4-(hydroxymethyl)benzenbornic acid (0.127 g, 1.2 mmol), Aliquat 336 (40

mg 0.08 mmol) and [Pd(PPh3)4] (22mg 0.02

mmol) was added a degassed mixture of 24 mL toluene and 16 mL of aqueous 2M

K2CO3. The mixture was vigorously stirred

at 85 ℃ for 48 h, cooled to room temperature and poured into 400 mL of methanol. The resulting precipitates were filtered and dried to obtain the solid product. The crude product was purified by soxhlet extraction with methanol to give the yellow powder (0.92g, 45 % yield) as final product. Anal. Calcd (assuming 6 repeating units

according to 1H NMR end-group analysis):

C, 91.40, H, 7.67. Found: C, 90.89, H, 8.05.

1H NMR (CDCl

(4)

aromatic protons), δ 7.39-8.12 (m, aromatic

protons), δ 4.91 (s, PhCH2O-), δ 2.05 (m, 4H,

-PhC–CH2-(CH2)4-CH3), δ 0.81-1.25 (m, 22

H, alkyl-H)) (see Figure 2.5). Mn = 3000,

Mw = 3900, Mw/Mn = 1.3 (GPC), Mn = 3000

(1H NMR).

Synthesis of PFA-in Macroinitiator. PFA-OH (0.46 g, 0.15 mmol), triethylamine (1.5 mL,

10 mmol), and dry CH2Cl2 (40 mL) were

placed in a 100 mL round-bottomed flask

and cooled to 0 before ℃ the addition of

2-bromoisobutyryl bromide (1.2 mL, 8.7 mmol). The whole system was then stirred vigorously under argon atmosphere before

raising temperature to 25 oC to stir overnight.

The solution was then extracted with water to remove the salt and the excess bromoisobutyryl bromide. The resulting mixtures were dried over anhydrous sodium sulfate, concentrated by rotary evaporator and precipitated from methanol to obtain the bromo-ended PFA macroinitiator. After filtration, the solid was rinsed with methanol sufficiently and passed through a short column using toluene as eluent. After being

dried under reduced pressure at 40 , ℃ 0.3g

of faint yellow product was obtained (75% in yield). Anal. Calcd (assuming 6 repeating

units according to 1H NMR end-group

analysis): C, 86.69, H, 7.33. Found: C, 85.99,

H, 7.15. 1H NMR (CDCl3, δ(ppm)): δ 8.65

(d, 2H, aromatic protons), δ 7.39-8.12 (m, aromatic protons), δ 5.40 (s, 0.66 H,

PhCH O-), δ 2.06 (m, 6H), δ 0.81-1.25 (m,

22 H, alkyl-H)) (see Figure 2.6). Mn = 3200,

Mw = 3850, Mw/Mn = 1.2 (GPC), Mn = 3200

(1H-NMR).

Synthesis of b-PMMA-PFA Block Copolymer. Typical reaction was performed with a glass tube charged with 0.03 g (0.01 mmol) of PFA-in macroinitiator and 2.0 mg (0.02 mmol) of CuCl. This glass tube was degassed through vacuum-argon cycles for three times to remove air and moisture before introducing o-dichlorobenzene (2 mL) and HMTETA (5.4 μL, 0.02 mmol) via syringes. After adding MMA (0.2 g, 2 mmol), the glass tube was immersed in an oil bath pre-set at 90 ℃ for 12 hr. After cooling to room temperature, the reaction mixture was passed through a column of neutral alumina to remove the catalysts. The polymer was precipitated into excess hexane

and dried under vacuum at 40 ℃. 1H NMR

(CDCl3, δ(ppm)): δ 8.65-7.40 (m, aromatic protons), δ 3.63 (s, 3H, COOCH3), δ 1.88 (s, 2H, -C(CH3)-CH2-), δ 1.88 (s, 3H, -C(CH3)-CH2-) (see Figure 2.7). Mn = 27000, Mw = 40500, Mw/Mn = 1.5 (GPC), 24200 (1H-NMR). 三、 結果與討論 首先,如流程一所示,將二種平面芳 香 族 發 光 體 單 體 茀 (fluorene) 及 蔥

(anthracene)以 Suzuki 偶合法(coupling)做

成 交 替 共 聚 物 (alternative

(5)

由於相鄰茀及蔥單元上二苯環鄰位(ortho-) 氫原子之空間障礙,形成扭曲(twisting)之 分子鍵形態,此扭曲分子鏈使得高分子鏈 不易相互靠近,從而降低其群聚之形成, 故其群聚程度將較均質高分子 PF〈見流程 一〉為低。進一步地,如流程二所示, 上 述之 Suzuki 偶合法亦可在加入適當之尾 端 基(end-group)後,得到聚合物起始劑 (macro-initiator) PFA-in,隨後進行原子轉

移 自 由 基 聚 (atom transfer radical

polymerization, ATRP),將聚甲基丙烯酸甲

(poly(methyl methacrylate), PMMA) 以

化學連結至中間之 a-PFA 鏈段,得到一柔 軟–剛硬–柔軟(flexible-rigid-flexible)之三 團 聯 共 聚 物 (triblock copolymer) b-PMMA-PFA,此三團聯共聚物中間為扭 曲高分子鏈 a-PFA,二邊為具阻隔作用之 PMMA 柔軟高分子鏈,故其較 a-PFA 之 群聚程度更低。 a-PFA 或 b-PMMA-PFA 之群聚程度 皆較均質高分子 PF 為低 ,但為增進其高 溫穩定度,本實驗室更進一步將其植入 PMMA 之交聯網狀結構中;如流程三所 示,將上述之高分子溶解於壓克力衍生單

體 (methyl methacrylate (MMA)/

di-trimethylolproane tetracrylate (DTTPT) 中,並加入光起始劑中,配置高分子/壓克 力單體溶液,並將此混和液予以紫外光光 照,以行硬化(cure)反應,以製造具交聯網 狀結構之固態薄膜複合材料(composite), 理論上,此非流動性網狀交聯結構可成功 地凍結住其上之螢光高分子分子鏈構形, 從而降低其高分子群聚程度。 有 關PF, a-PFA及b-PMMA-PFA之初 步比較見於圖一之放光光譜,其中大於500 nm以上之光譜為激發雙体及群聚之放光 所致,未處理之PF具最多比例之激發雙体 及群聚之放光,a-PFA次之,b-PMMA-PFA 最少。同時亦將所有高分子薄膜加熱至200 度經一、三、五小時之處理,或將其於此 溫度下定向剪切(shear)〈註:定向剪切可 增進分子鏈之同向排列,從而增進分子鏈 之相互作用及群聚程度〉,並觀察經此處理 後之光譜變化,其中PF之變化最大,其激 發 雙 体 及 群 聚 放 光 急 遽 加 大 ,a-PFA次 之,而b-PMMA-PFA之變化最少。所有放 光圖譜皆顯示激發雙体及群聚程度之增 加,皆導致放光強度之減少〈見圖譜中小 方格之插入圖〉,此結果顯示高分子放光之 熱穩定度與各自之化學結構有其相關性。 將PF, a-PFA及b-PMMA-PFA置於交 聯 網 狀 結 構(X-PMMA)所得之複合材料 〈以高分子/XPMMA表示之〉其放光行為 與原來高分子之比較見於圖二,所有複合 材料位於500 nm以上之放光皆較原來高 分子大幅減小,顯示網狀交聯體可成功地 凍結住螢光高分子之群聚。圖二a)之PF高 分子經導入網狀交聯體後其激發雙体及群 聚 放 光 大 幅 減 小 , 而 b-PMMA-PFA/X-PMMA複材經200度熱處

(6)

理五小時後之放光強度降低最少,故其為 最穩定之系統。 熱處理對PF, a-PFA, b-PMMA-PFA及 PF/X-PMMA, a-PFA/X-PMMA, b-PMMA-PFA/X-PMMA複合材料量子效 率之影響整理於表一,所有數據皆顯示網 狀 交 聯 體 可 有 效 增 進 其 熱 穩 定 度 , 而 b-PMMA-PFA 系 統 最 具 穩 定 度 , b-PMMA-PFA/X-PMMA於200度熱處理五 小時後其量子效率猶維持在69%。 四、結論 一、a-PFA 其相鄰二苯環鄰位氫原子之空 間障礙使其具有扭曲之分子鍵形態, 使得高分子鏈不易相互靠近,其群聚 程度較均質高分子PF 低;而 b-PMMA-PFA 此三團聯共其二邊更 具有具阻隔作用之PMMA 柔軟高分 子鏈,故其群聚程度亦較a-PFA 為低。 二、非流動性網狀交聯體可成功地凍結住 螢光高分子構形與高分子群聚程度。 三、網狀交聯體可成功地提升發光高分子 之熱穩定度,b-PMMA-PFA/X-PMMA 於200 度熱處理五小時後其量子效率 猶維持在69%。 五、參考文獻

[1] B. Valeur in “Molecular Fluoescence: Principles and Applications”, Wiley-VCH, New York, New York, 2001, P. 94).

[2] W. Minquan, Q. Guodong, W. Mang, F.

Xianping, H. Ananglian Mater. Sci. and Eng. (1996) B40, 67.

[3] M. Gratzel and J.K. Thomas in

“Modern Fluororescence Spectroscopy”, Vol. 2 E.L. Wehry, Ef., Plenum Press, New York, N.Y., 1976, p. 169.

[4] K. Kalyanasundaram, J.K. Thomas J. Amer. Chem. Soc. (1977) 99, 2039.

[5] Leclerc, M. J. Polym. Sci. Part A: Polym. Chem. 2001, 39, 2867.

[6] Neher, D. Macrom. Rapid Commun.

2001, 22, 1365.

[7] Scherf, U.; List, E. J. W. Adv. Mater.

2002, 14, 477.

[8] Pei, Q.; Yang, Y. J. Am. Chem. Soc. 1996, 118, 7416.

[9] Grice, A. W.; Bradley, D. D. C.; Bemius, M. T.; Inbasekaran, M.; Wu, W. W.; Woo, E. P. Appl. Phys. Lett. 1998, 73, 629.

[10] Lee, J. H.; Hwang, D. H. Chem. Commun. 2003, 2836.

[11] Chou, C. H.; Shu,C.F. Macromolecules

2002, 35, 9673.

[12] Li, J.; Bo, Z. Macromolecules 2004, 37, 2013.

[13] Pei, J.; Liu, X. L.; Chen, Z. K.; Zhang, X. H.; Lai, Y. H.; Huang, W. Macromolecules 2003, 36, 323.

[14] Yang, J.; Jiang, C. Zhang, Y.; Yang, R.; Yang, W. Hou, Q.; Cao, Y. Macromolecules

2004, 37, 1211.

[15] Chen, P.; Yang, G.; Liu, T.; Li, T.; Wang, M.; Huang, W. Polym. Int. 2006, 55, 473.

(7)

六、流程、圖及表

C6H13

C6H13

1-bromohexane Br

Br KOH, DMSO Br Brn-BuLi

C6H13 C6H13 B B 1 2 3 O O O O OB O OHC CH3 CH3 C6H13 C6H13 B B O O O O C6H13 C6H13 Br Br + C6H13 C6H13 K2CO3, toluene Pd(PPh3)4 C6H13 C6H13 C6H13 C6H13 B B OO O O + Br Br PF a-PFA 流程一: 單體 3 之合成及其與芳香族雙溴 化合物之共聚以得均質聚合物 PF 及 交替共聚物 a-PFA。 C6H13 C6H13 Br Br + + CH 2OH (HO)2B Suzuki reaction

4-HMBA, end-capping agent

C6H13 C6H13 CH2OH CuCl, HMTETA o-dichlorobenzene MMA (methyl methacrylate) n BiBB, TEA dichloromethane B O O B O O HOH2C C6H13 C6H13 n H2 C O C O Br H2 C O C O Br C6H13 C6H13 n H2 C O C O CH3 O OCH3 H2 C O C O CH3 O OCH3 PFA-OH PFA-in m m b-PMMA-PFA 流程二:聚合物起始劑PFA-in之合成及其 遂後之原子轉移自由基聚合以得三團聯共 聚物 b-PMMA-PFA。 C6H13 C6H13 n H2 C O C O CH3 O OCH3 H2 C O C O CH3 OOCH 3 m m b-PMMA-PFA S O O N H3C H2 C O O O O O O O H2 C O O H2C C CH3 O OCH3 MMA DTTPT + initiator UV-curing 流程三:聚合物/壓克力衍生單體/光起始 劑之照光硬化以得高分子複合材料。

a)

400 450 500 550 600 650 0 1 2 3 4 400 450 500 550 600 650 0 50 100 150 200 250 300 350 400 In ten s it y (a .u .) Wavelength (nm) Fresh film Shearing at 200 0 C Annealing at 200 0 C for 1 hr 3 hr 5 hr No rm a liz e d / PL i n te n s it y Wavelength (nm) Fresh film Shearing at 200 0C Annealing at 200 0C for 1 hr 3 hr 5 hr

b)

400 450 500 550 600 650 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 400 450 500 550 600 650 0 20 40 60 80 100 120 140 160 180 In te n s ity (a .u .) Wavelength (nm) Fresh film Shearing at 220 0 C Annealing at 220 0 C for 1 hr 3 hr 5 hr N o rm a liz e d / P L i n te n s it y Wavelength (nm) Fresh film Shearing at 220 0C Annealing at 220 0 C for 1 hr 3 hr 5 hr c) 400 450 500 550 600 650 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 400 450 500 550 600 650 0 100 200 300 400 In te n s it y (a .u .) Wavelength (nm) Fresh film Shearing at 200 0C Annealing at 200 0 C for 1 hr 3 hr 5 hr N o rm a liz e d / P L in te ns ity Wavelength (nm) Fresh film Shearing at 200 0C Annealing at 200 0C for 1 hr 3 hr 5 hr

圖一、a) PF , b) a-PFA及c) b-PMMA-PFA 薄膜經各種高溫處理後之放光光譜〈小方

格 之 光 譜 圖 為 未 歸 依(normalized) 之 圖

(8)

a) 300 350 400 450 500 550 600 650 0 1 2 3 4 N o rm a liz e d / P L in te n s it y 400 450 500 550 600 650 0 100 200 300 400 500 600 700 800 900 In te n s it y ( a .u .) Wavelength (nm) Fresh PF film Fresh PF/X-PMMA PF film after annealing at 2000C for 5 hr PF/X-PMMA after annealing at 2000C for 5 hr

N o rm al iz ed / A b so rb an c e Wavelength (nm) Fresh PF film Fresh PF/X-PMMA

PF film after annealing at 2000C for 5 hr PF/X-PMMA after annealing at 2000

C for 5 hr b) 300 350 400 450 500 550 600 650 0 1 2 3 4 400 450 500 550 600 650 0 100 200 300 400 In te n s it y ( a .u .) Wavelength (nm)

Fresh a-PFA film Fresh a-PFA/X-PMMA a-PFA film after annealing at 2000

C for 5 hr a-PFA/X-PMMA after annealing at 2000

C for 5 hr N o rm a liz e d / P L in te n s it y N o rm al iz ed / A b s o rb an ce Wavelength (nm)

Fresh a-PFA film Fresh a-PFA/X-PMMA

a-PFA film after annealing at 2000C for 5 hr a-PFA/X-PMMA after annealing at 2000

C for 5 hr c) 300 350 400 450 500 550 600 650 0 1 2 3 4 400 450 500 550 600 650 0 100 200 300 400 500 600 In te n s it y ( a .u .) Wavelength (nm)

Fresh b-PMMA-PFA film Fresh a-PMMA-PFA/X-PMMA b-PMMA-PFA film after annealing at 2000C for 5 hr

b-PMMA-PFA/X-PMMA after annealing at 2000C for 5 hr

N o rm a liz e d / P L in te n s it y N o rm al iz ed / A b so rb a n c e Wavelength (nm)

Fresh b-PMMA-PFA film Fresh b-PMMA-PFA/X-PMMA b-PMMA-PFA film after annealing at 2000

C for 5 hr

b-PMMA-PFA/X-PMMA after annealing at 2000 C for 5 hr 圖 二 、 a) PF/X-PMMA , b) a-PFA/X-PMMA 及 c) b-PMMA-PFA/X-PMMA薄膜經各種高溫 處理後之放光光譜〈小方格之光譜圖為未 歸依(normalized)之圖譜〉。 表一、熱處理對PF, a-PFA, b-PMMA-PFA 及 PF/X-PMMA, a-PFA/X-PMMA, b-PMMA-PFA/X-PMMA複合材料量子效 率之影響。 樣品 退火前 之量子 效率(%) 於200oC 五小 時後之量子效 率(%) PF 65 19 PF/X-PMMA 70 43 a-PFA 68 38 a-PFA/X-PMMA 73 52 b-PMMA-PFA 72 42 b-PMMA-PFA/X-PMMA 79 69

(9)

表二、於THF及甲苯製備之PMMA/PCA固 態膜之量子效率。

Solid films from solutions ofa [PMMA]/[PCA] = ФPL, THFb ФPL, Toluenec 2.5 M/0.0025 M (1000/1) 0.86 0.83 2.5 M/0.0075 M (330/1) 0.72 0.61 0.05 M/5*10-5 M (1000/1) 0.91 0.89 0.05 M/0.00015 M (330/1) 0.83d (0.72) 0.84d (0.74) 5×10-3 M/5×10-6 M (1000/1) 0.92 0.93 5×10-3 M/1.5×10-5 M (330/1) 0.86 0.88

a Solid film samples from the mother

solution states of different compositions.

b. Solid films prepared from THF solution.

c. Solid films prepared from toluene

solution.

d Solid films prepared from a

fast-evaporation process at high temperature.

數據

圖 二 、  a) PF/X-PMMA , b)  a-PFA/X-PMMA  及 c)  b-PMMA-PFA/X-PMMA薄膜經各種高溫 處理後之放光光譜〈小方格之光譜圖為未 歸依(normalized)之圖譜〉。  表一、熱處理對PF, a-PFA, b-PMMA-PFA 及 PF/X-PMMA, a-PFA/X-PMMA,  b-PMMA-PFA/X-PMMA複合材料量子效 率之影響。  樣品  退火前 之量子 效率(%)  於 200 o C 五小 時後之量子效率(%)  PF   65  19

參考文獻

相關文件

臺大機構典藏NTUR (National Taiwan University 二 Repository, http://ntur.lib.ntu.edu.tw) 經驗與協助推 動臺灣學術機構典藏TAIR (Taiwan Academic Institutional Repository,

Wayne Chang National Changhua University of Education- Master of Math Michael Wen National Kaohsiung Normal University - Bachelor of Math Peter Sun National Kaohsiung

If we recorded the monthly sodium in- take for each individual in a sample and his/her blood pressure, do individuals with higher sodium consumption also have higher blood

A Complete Example with equal sample size The analysis of variance indicates whether pop- ulation means are different by comparing the variability among sample means with

The natural structure for two vari- ables is often a rectangular array with columns corresponding to the categories of one vari- able and rows to categories of the second

Project 1.3 Use parametric bootstrap and nonparametric bootstrap to approximate the dis- tribution of median based on a data with sam- ple size 20 from a standard normal

• Many statistical procedures are based on sta- tistical models which specify under which conditions the data are generated.... – Consider a new model of automobile which is

∗ Suppose we want to determine if stocks picked by experts generally perform better than stocks picked by darts. We might conduct a hypothesis test to de- termine if the available