## Week 10

1.熟悉觀念

2.大量練習

3.教別人

4.上網看資料 outsourcing

The grade of exam is not good, mostly because too tight, not very familiar with computer operation, and I forgot to bring textbooks, so the test is not very ideal. Although I passed the exam there is still great room for improvement.
Progress is as follows:
1. be familiar with the concept of
2. a lot of practice
3. Teach others
4. Look online data outsourcing

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## week 9

1.13.30  complete homework version –> https://www.dropbox.com/s/1n3yxo3dznfrmvv/03154150week9.pdf?dl=0

(1)

H0= the mean height for females who prefer to sit in the back of the room ≤ average

H1= the mean height for females who prefer to sit in the back of the room > average

(4) p-value<α=0.05 reject the null hypothesis  the mean height for females who prefer to sit in the back of the room > average

2.13.44

(1)

H0=mean of placebo- mean of drug=0

H1= mean of placebo- mean of drug≠0

(4)p-value>α=0.05 do not reject the null hypothesis the claim that the drug could reduce jet lag couldn’t be accepted

3.13.45

(1)

(1)H0=blood pressure before-after=0

H1=blood pressure before-after≠0

(4)p-value<αreject the null hypothesis i.e. the blood pressure is higher before seeing the dentist

4.13.60

(1)

H0=men’s mean time of exercising=women’s mean time of exercising

H1= men’s mean time of exercising≠women’s mean time of exercising

(4) p-value<0.05 do not reject the null hypothesis i.e. the time of exercising has no association with gender

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## What are p-value, null value?

P-value

p-value is computed by assuming that the null hypothesis is true. When the p value is small enough, we reject the null hypothesis so as we accept the alternative hypothesis.”small enough” is defined as p value ≤α, where α =level of significance(usually0 .05)= 1-confidence interval

Null value

Ho:population parameter =null value

Null value is the specific number.If the parameter equals that number, then the null hypothesis is true.

Two-sided alternative hypothesis:

Ha:population parameter ≠null value

One-sided alternative hypothesis (choose one)

Ha: population parameter > null value

Ha: population parameter < null value

alternative hypothesis never includes the equals sign

Example 1 one-sided hypothesis test:

If researchers wanted to find out whether men have a lower mean pulse than women, the hypotheses for this one-sided hypothesis test would be:

Ho:μ1-μ2=0(μ1=μ2)

Ha:μ1-μ2<0(μ1<μ2)

μ1,μ2 are the mean pulse rates for the population of all men and all women, and the null value is 0.

Example 2

Suppose that a null hypothesis, in words, is that the mean weight for the population of newborn babies is the same in the United States as it is in England.

Ho:μ1-μ2=0

null value =0

Example 3

A legislator who wondered whether more than 50% of the voters in her district favored a law that would reduce the legal blood alcohol level that defines drunk driving. We let p= proportion of all voters in the district favoring the lower limit. A majority is p>0.5, so the null and alternative hypotheses for this situation may be written as:

Ho:p≤ 0.5(not a majority)

Ha:p>0.5(a majority)

The null value in this instance is pο=0.5

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## Week 7

1.上傳上課筆記     2.預習
(1)全文翻譯466頁最後一個Definition

The level of significance 顯著水準

(2)全文翻譯469頁Example 12.7全部

(3)全文翻譯470頁Definition

(4)全文翻譯471頁Definition

3.複習
(1)P.500, 12.6

a. H1:p=0.7

b.H1:p>0.45

c.H1:p<0.4

(2)P.501, 12.20

a.0.03

b.0.05

c.0.61

d.100

e.0.5

(3)P.508,12.104 based on Example 12.17 on Page 488

Step1: Determine the null and alternative hypothesis.

H0:p1-p2<=0(or p1>p2)

Ha:p1-p2>0(or p1<=p2)

Step2: Summarize the data into an appropriate test statistic after first verifying necessary data conditions are met.

• p^1= 0.25 p^2=0.09
• The sample statistic is p^1-p^2=0.25-0.09=0.16
• The combined proportion is p^=(783.81+250)/(8709+1000)=0.106
• The null standard error is null s.e.(p^1-p^2)=[0.106(1-0.106)(1/8709+1/1000)]^(1/2)=0.0102783 about 0.0103
• z=(Sample statistic-Null value)/Null standard error=0.16/0.0103=10.3129

Step3, 4, and 5:

Z score equals 10.3129 using table A.1 we could determine the probability 0.9999999 pvalue equals 1-0.999999=0.0000001

assume alpha value equals 0.05 which is larger than pvalue, so we could reject the null hypothesis. >>將內容用自己的手機、平版分享到.....

## week5

1.上課筆記上傳        2.預習
(1)全文翻譯462頁12.1至Lesson 1之間

1.決定用於推理母體的虛無假設與對立假設。

2.將所有重要的資料核對符合後，把資料總結為適當的測驗統計。

3.比較測驗統計與期望的所有可能性，看虛無假設是否屬實，以便找出P值。

4.用P值決定結果是否具統計顯著性。

5.將統計結論文字化。

(2)全文翻譯463頁definition

(3)全文翻譯464頁definition

(4)全文翻譯466頁definition

p值計算方式為:假設虛無假設為真，然後斷定檢定統計量為極值，或比以對立假設角度假設的檢定統計量更極端的觀察的檢定統計量機率。
3.複習      4.下週小考，範圍Ch10與Ch11(我有教的部分)

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## week 4

1.記得3/16筆記上網!    2.P.451 Q11.26完整計算過程 3.P.451 Q11.30完整計算過程  4.以PHStat4軟體做Q11.30 5.全文翻譯 P.439 Lesson 2至440頁Formula前  6.全文翻譯P.442 Pooled or Unpooled?

*如果兩個樣本標準差的巨大差異，來自群體的大樣本數，則合併版本的則傾向於產生較未合併更大的信賴區間，所以為較保守的差異估計值，就像下個例子所描述的。類似於我們為求一個比利，而用信賴區間內保守的邊際誤差值，用較保守的合併方式是可以被接受的。但是對於操做過大的區間卻不是好方法。

*另一方面，如果兩樣本標準差中較小的來自於較大的樣本，使用合併的方法可能會產生偏離的狹窄區間。

*一般來說，最好是用未合併的方式，除非樣本標準差非常相近。

7.詳細解釋下表黃色的數字如何得出 Sample Standard Deviation= σd/n^1/2

standard error of the mean=s/n^1/2=1.5206906/(9)^1/2

interval lower/upper limit= sample mean +- t*se=25.5+- 2.3036*0.506896878

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## Estimating Proportions with Confidence

1.忘了，記得3/10筆記上網!          2.page 403, 10.12 3.page 405, 10.28 4.上述兩題以PHStat4軟體做一次。  5. page 407, 10.58 6.全文翻譯p.416 Example 11.1

M1-M2=母體中獨居年長者血壓平均變化不同，有寵物與沒有的比較

7.page 449, 11.6 8.參考 Example 11.1，解page 453, 11.46 a與b。 >>將內容用自己的手機、平版分享到.....

## Week 2 hw

1. note     2.全文翻譯p.378上面3個黑點

3.全文翻譯p.379 Example 10.1上面2段

4.全文翻譯p.381-382 Example 10.2

1998年四月，聖母學院公眾輿論調查了883個隨機抽樣的美國成年人是否過敏。根據學院網站的報告，樣本中36%的人對於「你是否對任何東西過敏」回答是，所以樣本比例中，回答是的為p̂=0.36。我們用樣本資訊計算出95%信賴區間對母體參數p=美國成年人對某些東西過敏的比例的估計值。部分公式樣本統計量+-乘數*標準誤的值如下:

95%的信賴區間為0.36+-2*0.016等於0.36+-0.032或0.328 0.392(約33%到39%)

5.回答10.24(仿課本詳細過程) 6.回答10.54(仿課本詳細過程） >>將內容用自己的手機、平版分享到.....

## Week 2 pre

1.p.327 中間那3段

2.p.332 下半頁3段含公式

s.e.(p̂)=(p̂(1-p̂)/n)^1/2

01神奇的是，藉由單一的樣本決定出來這個值，用來估計所有可能樣本分配之標準本比例相當好用。因為我們已經知道實際平均值(p的比率)可以幾乎確定在觀察值p̂三個標準差以內，我們幾乎可以確定p的範圍在p̂+-3(s.e.)=0.39+-3(0.01)=0.39+-0.03。所以現在我們知道，實際支持候選人的比例幾乎可以確定介於0.36和0.42間。而唯一我們為了得知所需要的數值為樣本比例p̂還有樣本數n。

3.p.338 Definition下面那一段

4.p.339 最後一段含公式

s.e.(x̄)=s/n^1/2
s是樣本中觀察值的標準誤

5.p.348 中間之後的2段，最後一段不用

6.預習課程平台3/3筆記(3/1晚上上傳)

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## week1

notes

Chapter 9 Understanding Sampling Distributions: Statistics as Random Variables

9.1 Parameters, Statistics, and Statistical Inference

parameter 參數 : numerical summary of a population, value is fixed and unchanging

statistic or sample statistic 樣本統計量 : a numerical summary of a sample, value may be different for different samples

statistical inference 推論統計: 研究如何根據樣本數據去推斷總體數量特徵的方法。它是在對樣本數據進行描述的基礎上，對統計總體的未知數量特徵做出以機率形式表述的推斷。更概括地說，是在一段有限的時間內，通過對一個隨機過程的觀察來進行推斷的。The two most common procedures are to find confidence intervals and to conduct hypothesis tests.

confidence interval 信賴區間 :參數的真實值有一定機率落在測量結果的周圍的程度。信賴區間給出的是被測量參數的測量值的可信程度。這個機率被稱為信心水準。舉例來說，如果在一次大選中某人的支持率為55%，而信心水準0.95上的信賴區間是（50%,60%），那麼他的真實支持率有百分之九十五的機率落在百分之五十和百分之六十之間，因此他的真實支持率不足一半的可能性小於百分之2.5（假設分布是對稱的）。

hypothesis testing or significance testing 假設檢定 : 根據某些樣本，推論統計可以進行實驗的檢定某個假設 H1 是否可能，其方法是透過否定對立假設 H0，看看 H0 是否不太可能發生。

9.2 From Curiosity to Questions about Parameters

9.3 SD Module 0: An Overview of Sampling Distributions

9.4 SD Module 1: Sampling Distribution for One Sample Proportion

9.5 SD Module 2: Sampling Distribution for the Difference in Two Sample Proportions

9.6 SD Module 3: Sampling Distribution for One Sample Mean

9.7 SD Module 4: Sampling Distribution for the Sample Mean of Paired Differences

9.8 SD Module 5: Sampling Distribution for the Difference in Two Sample Means

9.9 Preparing for Statistical Inference: Standard Statistics

9.10 Generalizations beyond the Big Five

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