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Words 1849

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Words 1849

Pages 8

1.1.

x=

∑ xi i =1

N

N

1.2.

x=

∑ x i fi i =1 m i =1

m

∑ fi

2.

2.1.

xq =

i =1

∑ xi

N

N

2

2.2.

xq =

∑ x i fi

2 i =1 m

m

∑ fi i =1

3.

3.1.

x cub =

3 i =1

3 ∑ xi

N

N

3.2.

x cub = 3

∑ x i fi

3 i =1 m i =1

m

∑ fi

4. 4.1.

N xh = N 1 ∑ i =1 x i

4.2.

xh =

i =1 x i

∑

i =1 m 1

∑ fi

m

*

f i*

5.

Mo = L +

∆1. h ∆1 + ∆ 2

∆ 1 = f mo − f mo−1

∆ 2 = f mo − f mo +1

6.

N +1 h Me = L + − C me−1 2 f

7.

i.( N + 1) h Q i = L Qi + − C Qi−1 4 f Qi R = X max − X min

i = 1, 3

8.

VR =

R .100% x

9.

9.1.

δ=

i =1

∑ xi − x

N

9.2.

N

δ=

∑ x i − x fi i =1

m

∑ fi δ Vδ = .100% x i =1

m

9.3. 10.

10.1.

σ2 =

∑ ( x i − x) i =1

N

2

N

10.2.

σ2 =

2 ∑ ( x i − x) fi i =1

m

i =1

∑ fi

m

11.

11.1.

σ=

∑ ( x i − x) i =1

N

2

N

11.2.

σ= σ .100% x

i =1

2 ∑ ( x i − x) fi

m

i =1

∑ fi

m

11.3.

Vσ = Q= Q 3 − Q1 2

12.

VQ = x − Mo σ 3( x − Me) S2 = σ S1 =

Q 3 − Q1 .100% Q 3 + Q1

13. 14. 15. 15.1. k-

µk =

∑ ( x i − x )k i =1

N

N

15.2.

µk =

∑ (x i =1

m

i m

− x ) fi k i

∑f i =1

16.

S3 = E=

µ3 σ3

17.

µ4 −3 σ4

18. 18.1.

σ0

(θ = x → x 0 )

2

18.2.

(θ = p → p 0 ) n n = p(1 − p) n −1 n −1

n ∑ ( x i − x) $ σ=σ = n −1 n −1

19. 19.1.

$ σ=σ θ 19.2.

µθ =

20. 21. 21.1.

σ0 n 1− N n θ µθ =

σ0 n

∆ θ = zµ θ

21.2.

n=

22.

z ∆2 N + z σ 2 θ 0

2

σ2 N 0 2

n=

z2σ 2 0 2 ∆θ x − x0 σ0 n p − p0 σ0 n

t em [z em ] =

23.

t em [z em ] =

24.

t em [z em ] =

x 1 − x 2 n1 + n 2 − 2

(σ n

2 1 1

1 1 + σ2n 2 + 2 n n2 1

)

25.

t em [z em ] =

p1 − p 2 n1 + n 2 − 2

(p1q1n1 + p 2 q 2 n 2 )

1 1 + n1 n 2

26.

.

Fi =1 j =1

.

∑ y ij

: yi = j=1 ni

∑ ∑ y ij n m ni

ni m : y0 =

1 = i =m

∑ yi n i i =1

m

∑ ni σ2 M σ2 B

σ2 B

=

i =1 j =1

∑ ∑ (y ij − y i ) m ni

2

n−m

σ2 M

=

i =1

2 ∑ (y i − y 0 ) n i

m −1

$ y i = a + b. x i

Fem =

27. 27.1.

:

27.2.

:

∑ y i = a. N + b. ∑ x i 2 ∑ y i x i = a. ∑ x i + b. ∑ x i

:

27.3.

sy =

2 $ ∑ (yi − yi )

N s2 y σ2 y

28.

:

r = 1−

29. (

)

r=

∑ ( x i − x)( y i − y)

2 2 ∑ ( x i − x ) . ∑ ( y i − y)

30. 31.

:

D = r 2 .100% ρ =1− 6. ∑ d 2 i

N N −1

2

(

)

d i = N i( x) − N i( y) ad − bc (a + b)(c + d )(a + c)( b + d )

32.

“ϕ”

: ϕ=

33.

:

V=

ϕ2 min[( k 1 − 1), ( k 2 − 1)] ϕ2 = χ2 N

f −f $ 2 ij ij χ = ∑∑ $ f ij i =1 j=1 k2 f i* . f* j $ f ij = f i* = ∑ f ij N j=1 k1 k 2

(

)

2

k1 i =1

f* j = ∑ f ij

34. ) 34.1. )

y = i =1 N

34.2.

N −1 y i

∑ yi

N

1 y = i =m

∑ yi t i i =1

m

∑ ti

+ y i +1 ∑ 2 y = i =1 N −1

N −1 y

y=

i =1

∑

i

+ y i +1 ( t i +1 − t i ) 2

N −1 i =1

∑ (t i + 1 − t i )

35. 35.1.

∆ i / 1 = y i − y1

( )

∆ i / i −1 = y i − y i −1

35.2.

35.3.

∆=

y N − y1 N −1

36. 36.1.

36.2.

36.3.

Ti / 1 =

37. 37.1.

yi y1

Ti / i −1 =

yi y i −1

T = N −1

yN y1

∆ i / 1 (%) =

∆i / 1 .100 y1

37.2.

∆ i / i −1 (%) =

∆ i / i −1 .100 y i −1

∆ (%) = (T − 1).100

37.3.

38.

ˆ ˆ y i = y i −1 + ∆ = y1 + (i − 1).∆

39.

ˆ ˆ y i = y i −1.T = y1.T (i −1)

40. 40.1. 40.2. :

ˆ y = a + b.t

:

∑ y = a.N + b.∑ t ∑ yt = a.∑ t + b.∑ t 2

41. 41.1. 41.2. 41.3.

yi =

42.

y i ,1 + y i, 2 + ... + y i, N N

y0 =

y1 + y 2 + ... + y M M

I s (%) = i

(

yi .100 y0

)

42.1. (12-

42.2. )

i+5 yi − 6 + yi + 6 + ∑ yj 2 j= i − 5 ˆ yi = 12

yi =

41.3.

t =1

∑ y i, t

N yi .100 y0

N

42.3.

y 0 = i =1 M

43. 43.1.

∑ yi

M

I s (%) = i

( 43.2.

)

ˆ Y = a + bt t = 1,..., N b bm = 144

43.3.

yi =

43.4.

t =1

∑ y i, t

N

M

N

y i (k ) = y i − (i − 1)b m

y 0 = i =1 M

43.5. :

∑ yi

I s (%) = i

yi .100 y0

44. 44.1. 44.2. 44.3.

ip =

45. 45.1. 45.1.1.

p1 p0

iq =

q1 q0

i qp =

q1p1 q 0p0

( 45.1.2.

) 45.1.2.

Ip =

45.2. 45.1.1. (

∑ p1 ∑ p0

I p (q 0 ) =

( 45.1.2. )

∑ p1q 0 ∑ p0q 0

)

I p (q 1 ) =

∑ p1q1 ∑ p 0 q1

45.1.2.

Iq =

∑ q1 ∑q0

I q (p 0 ) =

∑ q1p 0 ∑ q0p0

I qp =

I q (p1 ) =

∑ q1p1 ∑ q 0 p1

45.3.

∑ q1p1 ∑ q 0p0

46.

∑ p1q1 ∑ p1q 0 I p(q1 ) = I p (q 0 ) .I str = I p(q 0 ). ∑p q : ∑p q 0 1 0 0

,

47.

I qp = I p (q 0 ) .I q (p1 ) = I p (q1 ).I q (p 0 )

48. 48.1. : 48.2. :

I p (q 0 ) =

∑ i p v0 = v0 ∑

∑

p1 .p 0 q 0 p0 ∑ p 0q 0 Ip = p1 p0

I p (q 1 ) =

∑ v1 = ∑ p1q1 1 p ∑ .v1 ∑ 0 .p1q1 ip p1 p0 =

49.

p1 =

∑ p1q1 ∑ q1

∑ p0q 0 ∑ q0

1.

α = 0,01

2,33 2,58

: , ., . , . “

α = 0,05

1,64 1,96

”, ., 1998.

2. :φ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

t-

α

0,10

6,31 2,92 2,35 2,13 2,02 1,94 1,90 1,86 1,83 1,81 1,80 1,78 1,77 1,76 1,75 1,75 1,74 1,73 1,73 1,73 1,72 1,72 1,71 1,71 1,71 1,71 1,70 1,70 1,70 1.69 1,64

0,05

12,71 4,30 3,18 2,78 2,57 2,45 2,36 2,31 2,26 2,23 2,20 2,18 2,16 2,14 2,13 2,12 2,11 2,10 2,09 2,09 2,08 2,07 2,07 2,06 2,06 2,06 2,05 2,05 2,05 2,04 1,96

0,02

31,82 6,97 4,54 3,75 3,37 3,14 3,00 2,90 2,82 2,76 2,72 2,68 2,65 2,62 2,60 2,58 2,57 2,55 2,54 2,53 2,52 2,51 2,50 2,49 2,49 2,48 2,47 2,47 2,46 2,46 2,33

0,01

63,66 9,92 5,84 4,60 4,03 3,71 3,50 3,36 3,25 3,17 3,11 3,05 3,01 2,99 2,95 2,92 2,90 2,88 2,86 2,85 2,83 2,82 2,81 2,80 2,79 2,78 2,77 2,76 2,76 2,75 2,58

φ

: , ., .

0,05

,

α

0,025

. “

0,01

”, ., 1998.

0,005

3.

F-

, α = 0,05

φ2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞

φ1

1

161,40 18,51 10,13 7,71 6,61 5,99 5,59 5,32 5,12 4,96 4,84 4,75 4,67 4,60 4,54 4,49 4,45 4,41 4,38 4,35 4,32 4,30 4,28 4,26 4,24 4,23 4,21 4,20 4,18 4,17 4,08 4,00 3,92 3,84

2

199,50 19,00 9,55 6,94 5,79 5,14 4,74 4,46 4,26 4,10 3,98 3,89 3,81 3,74 3,68 3,63 3,59 3,55 3,52 3,49 3,47 3,44 3,42 3,40 3,39 3,37 3,35 3,34 3,33 3,32 3,23 3,15 3,07 3,00

3

215,70 19,16 9,28 6,59 5,41 4,76 4,35 4,07 3,86 3,71 3,59 3,49 3,41 3,34 3,29 3,24 3,20 3,16 3,13 3,10 3,07 3,05 3,03 3,01 2,99 2,98 2,96 2,95 2,93 2,92 2,84 2,76 2,68 2,60

4

224,60 19,25 9,12 6,39 5,19 4,53 4,12 3,84 3,63 3,48 3,36 3,26 3,18 3,11 3,06 3,01 2,96 2,93 2,90 2,87 2,84 2,82 2,80 2,78 2,76 2,74 2,73 2,71 2,70 2,69 2,61 2,53 2,45 2,37

5

230,20 19,30 9,01 6,26 5,05 4,39 3,97 3,69 3,48 3,33 3,20 3,11 3,03 2,96 2,90 2,85 2,81 2,77 2,74 2,71 2,68 2,66 2,64 2,62 2,60 2,59 2,57 2,56 2,55 2,53 2,45 2,37 2,29 2,21…...

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...STAT 4220 Homework 2 Report Problem 1.22: a) Yˆ = 168.6 + 2.03X b) Yˆh = 168.6 + 2.03(40) = 168.6 + 81.2 = 249.8 c) 2.03 The population study is plastic hardness. The X is the elapsed time in hours and the Y is the hardness in Brinell units. The minimum unit was 196 with maximum to 253. The hours were 16 minimum and 40 maximum. The mean (average) was 225.6 for units and 28 for hours. The median was 226.5 units and 28 hours. The standard deviation of units with hour was 173.6. There was small variance large bias. Problem 1.28: a) a)Yˆ = 20517.6 + (-170.58)X No this equation does not fit well because there is not a line. b) 1)-170.58 2) Yˆh = 6871.2 3) ε10 = 1401.57 4) MSE= 5552112 The population was crime rates. The x is the percentage of the individuals in the county having at least high-school diploma and Y is the crime rate. The maximum percentage was 91 with the lowest 61. The crime rate was the maximum 14016 with the lowest 2105. The mean (average) was 7111 crime rate and 78.6 percent. The median was 79 percent and 6930 crime rate. The standard deviation of crime rate and percent was -6601.54. There was a Large variance small bias. Problem 1.31: In this problem the error will not include batch to batch variability and there will be a smaller variance from the original experiment. When you are going to use different batches there will not be a way to evaluate your results from the original experiment and the results there......

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...financial institutions it will be happy with the choice it makes to come or to stay with Wells Fargo. In the 1990’s Wells Fargo came out with a Vision and Values book but under Norwest Corporation at that time they were a small regional bank now Wells Fargo is a well known bank with a large global presence. Going back and keeping the traditions of each company they brought into make Wells Fargo what they are today is how the vision and values have all come about. Those beliefs are just as strong today as they were when they were first written down on a piece of paper. Staying true to them has helped Wells Fargo become known in every household, and where one in 600 US workers work. Wells Fargo is now home to 70 million customers. With stats like this, Wells Fargo is ranked in the top 10 publicly traded company according to Forbes magazine, this based on the sales, assets and market value. This is all attributed to going back to when they first started and kept the customers first. It didn’t matter how big Wells Fargo got there vision and values remained the same. Running head Wells Fargo 3 2. Analyze the five (5) forces of competition to determine how they impact the company. Wells Fargo had to compete against other banks. And depending on the size, the larger banks were trying to maximize customers as well. They......

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...83/84: STAT, TESTS, 1-PropZTest Po: assumed proportion (0.21) x: number of successes (732) n: total number of candies (3500) In the next line, select the correct alternative hypothesis/test, then Calculate, Enter. On the next screen, the second line shows the test. The next line has the test statistic. The next line has the p-value of the test (if less than significance level, reject null) The next two lines have and n. IF using StatCrunch, you will want Stat > Proportions > One Sample > with summary. In the first window, you will enter the same information as for part 3: number of the color (number of successes) and total number of candies (number of observations). Then click Next, and in the following window, enter the claimed proportion as a decimal in the box next to “null”, select the inequality that matches the alternative hypothesis and then click Calculate. The output will include the test statistic (Z-Stat) and the p-value. Hypothesis test results: p : proportion of successes for population H0 : p = 0.21 HA : p ≠ 0.21 Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 732 3500 0.20914286 0.006884766 -0.12449848 0.9009 Mean When you test for the mean number of candies per bag, you will need (sample mean), s (sample standard deviation) and n (total number of bags) as before. The test statistic is a z, because we have a large sample. Test statistic: IF using the TI 83/84: STAT, TESTS, Z-Test Input: Stats 0: ......

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...STAT 346/446 - A computer is needed on which the R software environment can be installed (recent Mac, Windows, or Linux computers are sufficient).We will use the R for illustrating concepts. And students will need to use R to complete some of their projects. It can be downloaded at http://cran.r-project.org. Please come and see me when questions arise. Attendance is mandatory. Topics covered in STAT 346/446, EPBI 482 Chapter 5 – Properties of a Random Sample Order Statistics Distributions of some sample statistics Definitions of chi-square, t and F distributions Large sample methods Convergence in probability Convergence in law Continuity Theorem for mgfs Major Theorems WLLN CLT Continuity Theorem Corollaries Delta Method Chapter 7 – Point Estimation Method of Moments Maximum Likelihood Estimation Transformation Property of MLE Comparing statistical procedures Risk function Inadmissibility and admissibility Mean squared error Properties of Estimators Unbiasedness Consistency Mean-squared error consistency Sufficiency (CH 6) Definition Factorization Theorem Minimal SS Finding a SS in exponential families Search for the MVUE Rao-Blackwell Theorem Completeness Lehmann-Scheffe Location and scale invariance Location and scale parameters Cramer-Rao lower bound Chapter 9 - Interval Estimation Pivotal Method for finding a confidence interval Method for finding the “best” confidence interval Large sample confidence......

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...test results: μ1 : mean of Credit Balance($) μ2 : mean of Size μ1 - μ2 : mean difference H0 : μ1 - μ2 = 0.05 HA : μ1 - μ2 ≠ 0.05 (with pooled variances) Difference | Sample Mean | Std. Err. | DF | T-Stat | P-value | μ1 - μ2 | 3967.04 | 131.7902 | 98 | 30.100796 | <0.0001 | Base on my findings I believe that size is a great indictor of helping find credit balance. Here is why, you can look at the average size of a household and see the cost to run that house household. The bigger the household size the more money it cost to operate that household. I think that this what the all the test illustrates when you look at each figure. APPENDIX C Simple linear regression results: Dependent Variable: Size Independent Variable: Credit Balance($) Size = -2.1549776 + 0.0014041137 Credit Balance($) Sample size: 50 R (correlation coefficient) = 0.7524 R-sq = 0.56616867 Estimate of error standard deviation: 1.1572698 Parameter estimates: Parameter | Estimate | Std. Err. | DF | 95% L. Limit | 95% U. Limit | Intercept | -2.1549776 | 0.7231484 | 48 | -3.6089647 | -0.70099014 | Slope | 0.0014041137 | 1.7740639E-4 | 48 | 0.0010474143 | 0.0017608132 | Analysis of variance table for regression model: Source | DF | SS | MS | F-stat | P-value | Model | 1 | 83.89487 | 83.89487 | 62.64207 | <0.0001 | Error | 48 | 64.28513 | 1.3392736 | | | Total | 49 | 148.18 | | | | APPENDIX D When you look at the intervals of the Credit......

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