# PSYCHOLOGICAL STATISTICS

Save this PDF as:
Size: px
Start display at page:

## Transcription

2 8. Which of the followig is a ull hypothesis? There is sigificat relatioship betwee the variable X ad Y. b) There is o geder differece i the mea scores of mechaical aptitude. c) There is sigificat effect of itelligece o achievemet. 9. The opposite of ull hypothesis is kow as Directioal hypothesis b) Statistical hypothesis c) Alterate hypothesis d) Composite hypothesis 0. Which of the followig is a alterate hypothesis? There is sigificat geder differece i the mea scores of mechaical aptitude. b) There is o sigificat relatioship betwee achievemet ad previous kowledge. c) There is o sigificat effect of itelligece o creativity.. Some statemet or assertio above a populatio is kow as Uique statemet b) a stadard statemet c) Stadard hypothesis d) a statistical hypothesis. A hypothesis i which there is o idicatio of directio of chage or relatio is called a directioal hypothesis b) o directioal hypothesis c) alterate hypothesis 3. Tests used to test o directioal hypothesis are Oe tailed tests b) Two-tailed tests c) Three tailed tests d) Four tailed tests 4. For testig H 0 : = agaist H 0 : we have the Oe tailed test b) Two-tailed test c) Three tailed test 5. The alterate hypothesis for the ull hypothesis H 0 : < is H : > b) H : = c) H : < d) H : > 6. For testig which of the followig hypothesis two-tailed test is used? H 0 : < agaist H : > b) H 0 : > agaist H : < c) H 0 : = agaist H : Psychological Statistics Page

3 7. For testig which of the followig hypothesis oe tailed test is used? o directioal hypothesis b) directioal hypothesis c) alterate hypothesis d) composite hypothesis 8. For testig which of the followig hypothesis oe tailed test is used? There is o sigificat geder differece i the mea scores of axiety. b) There is sigificat relatioship betwee variables X ad Y. c) Experimetal group has a higher mea Y score tha the cotrol group after the treatmet. d) There is o sigificat differece i mea Y scores of cotrol ad experimetal groups after the treatmet. 9. Statistical tests are desiged to test the Alterate hypothesis b) Statistical hypothesis c) Composite hypothesis d) Null hypothesis 0. Which of the followig hypothesis are accepted or rejected? alterate hypothesis b) statistical hypothesis c) composite hypothesis d) ull hypothesis. Hypothesis testig deals with Predictio of populatio values based o sample values b) predictio of sample values based o populatio values c) Both ( ad (b). Which of the followig is type I error? The error of acceptig H 0 whe H 0 is true. b) The error of rejectig H 0 whe H 0 is false c) The error of rejectig H 0 whe H 0 is true d) The error of acceptig H 0 whe H 0 is false. 3. Which of the followig is type II errors? The error of acceptig H 0 whe H 0 is true b) The error of rejectig H 0 whe H 0 is false c) The error of acceptig H 0 whe H 0 is false d) The errors of rejectig H 0 whe H 0 is true 4. The probability of type I error is Power of the test b) Statistical sigificace c) Level of sigificace Psychological Statistics Page 3

4 5. The probability of type II error is deoted by b) c) d) 6. Which of the followig statemets is icorrect? As probability of Type I error icreases, probability of type II error also icreases. b) As the probability of Type I error decreases, the probability of type II error icreases. c) As the probability of Type II error decreases, the probability of Type I error icreases. 7. Samplig distributios are distributios formed by Populatio values b) Sample values c) Parameters 8. Samplig distributio of mea values is distributio formed by Populatio mea values b) Sample correlatio values c) Sample mea values d) Populatio correlatio values 9. Which of the followig statemets is true about samplig distributios? Distributios formed by sample values b) Formed from a populatio distributio kow or assumed. c) A umber of samplig distributios is possible from a populatio. 30. Which of the followig is stadard error? Mea of samplig distributio b) Stadard deviatio of populatio distributio c) Mea of populatio distributio d) Stadard deviatio of sample distributio. 3. Which oe of the followig idicates stadard error of samplig distributio of mea? b) c) d) N N N N 3. Which of the followig are true about stadard error? Gives a idea about ureliability of the sample b) Gives a idea about cofidece limits of parameter values c) Both ( ad (b) 33. Which of the followig is a statistically large sample? 9 b) 45 c) 6 Psychological Statistics Page 4

5 34. The term statistical sigificace refers to How importat the data are for research o the topic b) The coclusio that there are o reasoable alterative explaatio c) The represetativeess of the sample d) The iferece that the observed effects are ulikely to be due to chace. 35. If we take level of sigificace as 0.0 the the cofidece limit will be % b) 0% c) 99% d) 00% 36. Critical ratio for large idepedet sample is give by the formula z = c) z = Mea Stadard Deviatio Differece betwee Meas SE of the differece b) z = Differece betwee Meas Stadard Error 37. Z =.03 while testig H 0 : = agaist H :. The which of the followig is true? H 0 is rejected at 0.05 level b) H 0 is accepted at 0.05 level c) Both ( ad (b) 38. Followig data is related to emotioal itelligece of two groups A ad B. Mea SD N Group A Group B The the critical ratio is give by.53 b).98 c) The critical ratio is foud to be.63 while testig H 0 : = agaist H :. The which of the followig statemets is true? H 0 is accepted at 0.05 level b) H 0 is rejected at 0.05 level c) H 0 is accepted at 0.0 level d) H 0 is rejected at 0.0 level 40. While dealig with small samples, preferece is give to estimatig the populatio value b) testig a give hypothesis c) both ( ad (b) d) oe of these 4. The critical regio is the regio of rejectio of H 0 whe H 0 is false b) acceptace of H 0 whe H 0 is false c) rejectio of H 0 whe H 0 is true 4. Studet was the pe ame of Ramauja b) Gosset c) Garrette Psychological Statistics Page 5

6 43. Uder which of the followig circumstaces t distributio is used? Sample size less tha or equal to 30 b) Populatio stadard deviatio is ukow c) Both ( ad (b) 44. Formula for calculatig t statistic to test the sigificace of mea is give by X μ X μ X μ X μ b) c) c) S S S S 45. I the formula for calculatig t statistic, the letter S stads for X X X X X X b) c) d) Which of the followig are the properties of t distributio? rages from mius ifiity to plus ifiity b) t distributio does ot vary with c) Both ( ad (b) 47. Which of the followig is true about t distributio? Symmetrical b) Negatively skewed b) Positively skewed c) Noe of these 48. As sample size icreases the t distributio approaches a X X Biomial distributio b) Gamma distributio c) Poisso distributio d) Normal distributio 49. The degrees of freedom for which the tabled t value is foud for test of sigificace of mea is give by b) c) 50. If the calculated t value is less tha t 0.05 (tabled value of t) the which of the followig coclusios ca be made about the hypothesis H 0 : X μ, where is populatio mea. H 0 is accepted at 0.0 level b) H 0 is accepted at 0.05 level b) H 0 is rejected at 0.05 level c) Noe of these 5. To test whether two meas (Small idepedet samples) differ sigificatly, t ca be calculated usig the formula c) X X X X X X X X b) X X X X X X - X X X X Psychological Statistics Page 6

7 5. The degrees of freedom for testig sigificace of differece betwee two meas for small idepedet samples is + b) + - c) If the samples are depedet, the differece betwee mea ca be tested usig the formula. d t = N s d b) t = s c) d s d d) s 54. Which of the followig is the t value for the followig data (small idepedet samples) X =, X =, =5, =7, s =., s = b) 0.35 c) 0.89 d) To test the sigificace of correlatio coefficiet, which of the followig formula is used? r t = r r c) r r b) r r d) r 56. Degrees of freedom for testig the sigificace of correlatio coefficiet is calculated usig the formula b) - c) -3 d) Normal distributio was origially ivestigated by Gauss b) Laplace c) DeMoivre 58. Normal distributio was defied specially by Laplace b) Gauss c) DeMoivre 59. Which of the followig is sigificace of ormal distributio i statistical aalysis? May of the depedet variables are commoly assumed to be ormally distributed b) May of the statistical techiques i iferetial statistics assumes ormality of variable. c) The theoretical distributio of the hypothetical set of sample meas is approximately ormal. 60. Which of the followig is icorrect about ormal distributio? It is symmetrical with respect to the ordiate at mea. b) Mea, Media ad Mode coicide c) Ordiate is miimum at the mea Psychological Statistics Page 7

8 6. A ormal curve shows. a distributio of metally ormal persos. populatio distributed equally i various parts 3. greater percetage of cases distributed about the mea score 4. lesser percetage of cases belogig to extreme scores Oly ad are true b) Oly 3 ad 4 are true c) all are true d) all are false 6. A mesokurtic distributio curve is a ormal probability curve b) bell shaped curve c) both ( ad (b) 63. A leptokurtic distributio shows A bell shaped curve b) Skewess c) Steep rise i the middle d) Upto some extet it shows all of these 64. Mathematically a ormal distributio is defied as y = c) y = e σ π e σ π x μ x μ σ b) y = d) y = e π Psychological Statistics Page 8 x μ σ e σ π xμ 65. The area uder the ormal curve betwee the ordiates x = - ad x = + is 68.6% b) 95.44% c) 34.3% 66. The area uder the ormal curve betwee the ordiates x = - ad x = + is 68.6% b) 95.44% c) 99% 67. The area uder the ormal curve betwee the ordiates x = - 3 ad x = +3 is 68.6% b) 95.44% c) 99.73% d) 90% 68. The ormal curve is symmetric with respect to x = b) x = c) x = σ σ 69. Exact cofidece limit whe the populatio is ormal, for mea is σ 95% cofidece limit = x +.96 σ b) 99% cofidece limit = = x +.58 c) a ad b both

10 79. Which of the followig statemets is true about platykurtic curve as compared to ormal curve? Flatter b) broader cetral positio c) Lower tails 80. Which of the followig is a measure of kurtosis? Quartile Deviatio P75 P5 Stadard Deviatio P75 P5 b) c) d) P 90 P 0 4 P 90 P A distributio is leptokurtic if the calculated value of kurtosis i terms of percetile is Equal to 0.63 b) Less tha 0.63 c) Greater tha A distributio is platykurtic if the calculated value of kurtosis i terms of percetile is equal to zero b) less tha 0.63 c) greater tha 0.63 d) equal to ANOVA test is based o Variace ratio b) Probability ratio c) radom sample 84. ANOVA is used whe There are more tha two groups b) There is oly two groups to be compared. c) Sigificat differece betwee two meas is to be foud 85. Which of the followig test is used i ANOVA t-test b) z-test c) F-test 86. I ANOVA, F-value is calculated usig which of the followig formula? Variace withi groups Variace betwee groups b) Variace betwee groups Variace withi groups c) Both ( ad (b) 87. The assumptio basic to Aalysis of Variace is Populatio distributio of the depedet variable follow ormality b) Subgroups uder study have same variability c) Groups draw o certai criteria, radomly selected from the sub populatio. 88. Which of the followig is the correct sequece of steps for oe way ANOVA? ) Total sum of squares ) Correctio 3) Withi sum of squares 4) Betwee sum of squares,, 3, 4 b) 3,, 4, c) 4, 3,, d),, 4, The mea sum of squares (MS) is The sum of squares multiplied by its degrees of freedom b) The sum of squares divided by its degrees of freedom c) The sum of squares mius its degrees of freedom d) The sum of squares plus its degrees of freedom Psychological Statistics Page 0

11 90. The F value for oe-way ANOVA is give by the formula b w b) df df b b w w c) df df 9. I ANOVA idepedet variables are called Categories b) Levels c) Factors 9. I ANOVA differet categories of a idepedet variable are called. w w b b d) factors b) levels c) groups d) blocks 93. If there are more tha oe idepedet variables we use Oe Way ANOVA b) ANOVA for factorial desig c) Both ( ad (b) 94. I oe way ANOVA how may F values are calculated b) 3 c) d) If there are two idepedet variables the how may effects are foud i ANOVA? b) c) 3 d) Which of the followig statemets are true about Two-way ANOVA with x 3 desig. There are two idepedet variables b) The first idepedet variable has two levels c) The secod idepedet variable has 3 levels 97. For testig the sigificace of differece betwee meas, ANOVA aalyses Meas b) Stadard deviatios c) Correlatios Coefficiets d) Variaces 98. I oe way ANOVA, if the calculated F value is greater tha the tabled value of F, the Mea differece betwee all pairs of groups will be sigificat b) Mea differece is ot sigificat c) Mea differece betwee more tha two groups i the set will be sigificat d) Mea differece betwee atleast two groups i the set will be sigificat 99. Which of the followig is true about ANOVA? It is a o parametric test b) Homogeeity of variace is ot a basic assumptio c) It is a parametric test d) Assumptio of ormality is ot ecessary w b 00. The calculated value of kurtosis i terms of percetile for a give data is foud to be 0.3, the the distributio is Mesokurtic b) Leptokurtic c) Platykurtic Psychological Statistics Page

12 ANSWER KEY. B. A 4. C 6. B 8. B. C. C 4. B 6. C 8. C 3. B 3. C 43. C 63. C 83. A 4. C 4. C 44. D 64. D 84. A 5. A 5. B 45. C 65. A 85. C 6. D 6. A 46. A 66. B 86. B 7. D 7. B 47. A 67. C 87. D 8. B 8. C 48. D 68. B 88. D 9. C 9. D 49. C 69. C 89. B 0. A 30. D 50. B 70. D 90. B. D 3. B 5. C 7. D 9. C. B 3. C 5. C 7. B 9. B 3. B 33. B 53. A 73. C 93. B 4. B 34. D 54. C 74. D 94. C 5. A 35. C 55. A 75. D 95. C 6. C 36. C 56. D 76. D 96. D 7. B 37. A 57. C 77. C 97. D 8. C 38. C 58. A 78. D 98. D 9. D 39. D 59. D 79. D 99. C 0. A 40. B 60. C 80. A 00. C Reserved Psychological Statistics Page

### Z-TEST / Z-STATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown

Z-TEST / Z-STATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large T-TEST / T-STATISTIC: used to test hypotheses about

### Inference on Proportion. Chapter 8 Tests of Statistical Hypotheses. Sampling Distribution of Sample Proportion. Confidence Interval

Chapter 8 Tests of Statistical Hypotheses 8. Tests about Proportios HT - Iferece o Proportio Parameter: Populatio Proportio p (or π) (Percetage of people has o health isurace) x Statistic: Sample Proportio

### Hypothesis testing. Null and alternative hypotheses

Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

### One-sample test of proportions

Oe-sample test of proportios The Settig: Idividuals i some populatio ca be classified ito oe of two categories. You wat to make iferece about the proportio i each category, so you draw a sample. Examples:

### 1. C. The formula for the confidence interval for a population mean is: x t, which was

s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : p-value

### Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

### I. Chi-squared Distributions

1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

### A Test of Normality. 1 n S 2 3. n 1. Now introduce two new statistics. The sample skewness is defined as:

A Test of Normality Textbook Referece: Chapter. (eighth editio, pages 59 ; seveth editio, pages 6 6). The calculatio of p values for hypothesis testig typically is based o the assumptio that the populatio

### Lesson 17 Pearson s Correlation Coefficient

Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

### Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

### GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

### MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)

MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:

### Statistical inference: example 1. Inferential Statistics

Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either

### The following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles

The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio

### Lesson 15 ANOVA (analysis of variance)

Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

### 1 Correlation and Regression Analysis

1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

### Chapter 7: Confidence Interval and Sample Size

Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum

### University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

### 5: Introduction to Estimation

5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

### Output Analysis (2, Chapters 10 &11 Law)

B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

### 15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011

15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes high-defiitio

### Determining the sample size

Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

### TI-83, TI-83 Plus or TI-84 for Non-Business Statistics

TI-83, TI-83 Plu or TI-84 for No-Buie Statitic Chapter 3 Eterig Data Pre [STAT] the firt optio i already highlighted (:Edit) o you ca either pre [ENTER] or. Make ure the curor i i the lit, ot o the lit

### Sampling Distribution And Central Limit Theorem

() Samplig Distributio & Cetral Limit Samplig Distributio Ad Cetral Limit Samplig distributio of the sample mea If we sample a umber of samples (say k samples where k is very large umber) each of size,

### Chapter 14 Nonparametric Statistics

Chapter 14 Noparametric Statistics A.K.A. distributio-free statistics! Does ot deped o the populatio fittig ay particular type of distributio (e.g, ormal). Sice these methods make fewer assumptios, they

### Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

### Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

### Practice Problems for Test 3

Practice Problems for Test 3 Note: these problems oly cover CIs ad hypothesis testig You are also resposible for kowig the samplig distributio of the sample meas, ad the Cetral Limit Theorem Review all

### Confidence intervals and hypothesis tests

Chapter 2 Cofidece itervals ad hypothesis tests This chapter focuses o how to draw coclusios about populatios from sample data. We ll start by lookig at biary data (e.g., pollig), ad lear how to estimate

### CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

STATISTICAL METHODS FOR BUSINESS UNIT 7: INFERENTIAL TOOLS. DISTRIBUTIONS ASSOCIATED WITH SAMPLING 7.1.- Distributios associated with the samplig process. 7.2.- Iferetial processes ad relevat distributios.

### A Mathematical Perspective on Gambling

A Mathematical Perspective o Gamblig Molly Maxwell Abstract. This paper presets some basic topics i probability ad statistics, icludig sample spaces, probabilistic evets, expectatios, the biomial ad ormal

### Math C067 Sampling Distributions

Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters

### , a Wishart distribution with n -1 degrees of freedom and scale matrix.

UMEÅ UNIVERSITET Matematisk-statistiska istitutioe Multivariat dataaalys D MSTD79 PA TENTAMEN 004-0-9 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multivariat dataaalys D, 5 poäg.. Assume that

### Now here is the important step

LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest"

### Mann-Whitney U 2 Sample Test (a.k.a. Wilcoxon Rank Sum Test)

No-Parametric ivariate Statistics: Wilcoxo-Ma-Whitey 2 Sample Test 1 Ma-Whitey 2 Sample Test (a.k.a. Wilcoxo Rak Sum Test) The (Wilcoxo-) Ma-Whitey (WMW) test is the o-parametric equivalet of a pooled

### Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

### Confidence Intervals for One Mean

Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

### STA 2023 Practice Questions Exam 2 Chapter 7- sec 9.2. Case parameter estimator standard error Estimate of standard error

STA 2023 Practice Questios Exam 2 Chapter 7- sec 9.2 Formulas Give o the test: Case parameter estimator stadard error Estimate of stadard error Samplig Distributio oe mea x s t (-1) oe p ( 1 p) CI: prop.

### Chapter 7 - Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas:

Chapter 7 - Samplig Distributios 1 Itroductio What is statistics? It cosist of three major areas: Data Collectio: samplig plas ad experimetal desigs Descriptive Statistics: umerical ad graphical summaries

### Confidence Intervals

Cofidece Itervals Cofidece Itervals are a extesio of the cocept of Margi of Error which we met earlier i this course. Remember we saw: The sample proportio will differ from the populatio proportio by more

### Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

### 0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5

Sectio 13 Kolmogorov-Smirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.

### THE TWO-VARIABLE LINEAR REGRESSION MODEL

THE TWO-VARIABLE LINEAR REGRESSION MODEL Herma J. Bieres Pesylvaia State Uiversity April 30, 202. Itroductio Suppose you are a ecoomics or busiess maor i a college close to the beach i the souther part

### THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n

We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample

### Chapter 7 Methods of Finding Estimators

Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of

### Hypothesis testing using complex survey data

Hypotesis testig usig complex survey data A Sort Course preseted by Peter Ly, Uiversity of Essex i associatio wit te coferece of te Europea Survey Researc Associatio Prague, 5 Jue 007 1 1. Objective: Simple

### Multi-server Optimal Bandwidth Monitoring for QoS based Multimedia Delivery Anup Basu, Irene Cheng and Yinzhe Yu

Multi-server Optimal Badwidth Moitorig for QoS based Multimedia Delivery Aup Basu, Iree Cheg ad Yizhe Yu Departmet of Computig Sciece U. of Alberta Architecture Applicatio Layer Request receptio -coectio

### Unit 8: Inference for Proportions. Chapters 8 & 9 in IPS

Uit 8: Iferece for Proortios Chaters 8 & 9 i IPS Lecture Outlie Iferece for a Proortio (oe samle) Iferece for Two Proortios (two samles) Cotigecy Tables ad the χ test Iferece for Proortios IPS, Chater

### This document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.

SPC Formulas ad Tables 1 This documet cotais a collectio of formulas ad costats useful for SPC chart costructio. It assumes you are already familiar with SPC. Termiology Geerally, a bar draw over a symbol

### Data Analysis and Statistical Behaviors of Stock Market Fluctuations

44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:

### 1 Computing the Standard Deviation of Sample Means

Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

### Descriptive Statistics

Descriptive Statistics We leared to describe data sets graphically. We ca also describe a data set umerically. Measures of Locatio Defiitio The sample mea is the arithmetic average of values. We deote

### Section 11.3: The Integral Test

Sectio.3: The Itegral Test Most of the series we have looked at have either diverged or have coverged ad we have bee able to fid what they coverge to. I geeral however, the problem is much more difficult

### Properties of MLE: consistency, asymptotic normality. Fisher information.

Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout

### Hypergeometric Distributions

7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you

### Normal Distribution.

Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued

### Overview of some probability distributions.

Lecture Overview of some probability distributios. I this lecture we will review several commo distributios that will be used ofte throughtout the class. Each distributio is usually described by its probability

### Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

### Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean

1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

### Example: Probability (\$1 million in S&P 500 Index will decline by more than 20% within a

Value at Risk For a give portfolio, Value-at-Risk (VAR) is defied as the umber VAR such that: Pr( Portfolio loses more tha VAR withi time period t)

### Hand-book on STATISTICAL DISTRIBUTIONS for experimentalists

Iteral Report SUF PFY/96 Stockholm, December 996 st revisio, 3 October 998 last modificatio September 7 Had-book o STATISTICAL DISTRIBUTIONS for experimetalists by Christia Walck Particle Physics Group

### OMG! Excessive Texting Tied to Risky Teen Behaviors

BUSIESS WEEK: EXECUTIVE EALT ovember 09, 2010 OMG! Excessive Textig Tied to Risky Tee Behaviors Kids who sed more tha 120 a day more likely to try drugs, alcohol ad sex, researchers fid TUESDAY, ov. 9

### Research Method (I) --Knowledge on Sampling (Simple Random Sampling)

Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact

### Central Limit Theorem and Its Applications to Baseball

Cetral Limit Theorem ad Its Applicatios to Baseball by Nicole Aderso A project submitted to the Departmet of Mathematical Scieces i coformity with the requiremets for Math 4301 (Hoours Semiar) Lakehead

### SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

### Chapter XIV: Fundamentals of Probability and Statistics *

Objectives Chapter XIV: Fudametals o Probability ad Statistics * Preset udametal cocepts o probability ad statistics Review measures o cetral tedecy ad dispersio Aalyze methods ad applicatios o descriptive

### Incremental calculation of weighted mean and variance

Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

### Basic Data Analysis Principles. Acknowledgments

CEB - Basic Data Aalysis Priciples Basic Data Aalysis Priciples What to do oce you get the data Whe we reaso about quatitative evidece, certai methods for displayig ad aalyzig data are better tha others.

### Soving Recurrence Relations

Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

### CONTROL CHART BASED ON A MULTIPLICATIVE-BINOMIAL DISTRIBUTION

www.arpapress.com/volumes/vol8issue2/ijrras_8_2_04.pdf CONTROL CHART BASED ON A MULTIPLICATIVE-BINOMIAL DISTRIBUTION Elsayed A. E. Habib Departmet of Statistics ad Mathematics, Faculty of Commerce, Beha

### UM USER SATISFACTION SURVEY 2011. Final Report. September 2, 2011. Prepared by. ers e-research & Solutions (Macau)

UM USER SATISFACTION SURVEY 2011 Fial Report September 2, 2011 Prepared by ers e-research & Solutios (Macau) 1 UM User Satisfactio Survey 2011 A Collaboratio Work by Project Cosultat Dr. Agus Cheog ers

### Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

### Quadrat Sampling in Population Ecology

Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may

### In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

### BASIC STATISTICS. f(x 1,x 2,..., x n )=f(x 1 )f(x 2 ) f(x n )= f(x i ) (1)

BASIC STATISTICS. SAMPLES, RANDOM SAMPLING AND SAMPLE STATISTICS.. Radom Sample. The radom variables X,X 2,..., X are called a radom sample of size from the populatio f(x if X,X 2,..., X are mutually idepedet

### Parametric (theoretical) probability distributions. (Wilks, Ch. 4) Discrete distributions: (e.g., yes/no; above normal, normal, below normal)

6 Parametric (theoretical) probability distributios. (Wilks, Ch. 4) Note: parametric: assume a theoretical distributio (e.g., Gauss) No-parametric: o assumptio made about the distributio Advatages of assumig

### A Recursive Formula for Moments of a Binomial Distribution

A Recursive Formula for Momets of a Biomial Distributio Árpád Béyi beyi@mathumassedu, Uiversity of Massachusetts, Amherst, MA 01003 ad Saverio M Maago smmaago@psavymil Naval Postgraduate School, Moterey,

### Modified Line Search Method for Global Optimization

Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

### An optical illusion. A statistical illusion. What is Statistics? What is Statistics? An Engineer, A Physicist And A Statistician.

A optical illusio Yalçı Akçay CASE 7 56 yakcay@ku.edu.tr A statistical illusio A Egieer, A Physicist Ad A Statisticia Real estate aget sellig a house to a sob customer: typical mothly icome i the eighborhood

### Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships

Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the

### Present Values, Investment Returns and Discount Rates

Preset Values, Ivestmet Returs ad Discout Rates Dimitry Midli, ASA, MAAA, PhD Presidet CDI Advisors LLC dmidli@cdiadvisors.com May 2, 203 Copyright 20, CDI Advisors LLC The cocept of preset value lies

### Exploratory Data Analysis

1 Exploratory Data Aalysis Exploratory data aalysis is ofte the rst step i a statistical aalysis, for it helps uderstadig the mai features of the particular sample that a aalyst is usig. Itelliget descriptios

### CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

### A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design

A Combied Cotiuous/Biary Geetic Algorithm for Microstrip Atea Desig Rady L. Haupt The Pesylvaia State Uiversity Applied Research Laboratory P. O. Box 30 State College, PA 16804-0030 haupt@ieee.org Abstract:

### PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics

### 7. Concepts in Probability, Statistics and Stochastic Modelling

7. Cocepts i Probability, Statistics ad Stochastic Modellig 1. Itroductio 169. Probability Cocepts ad Methods 170.1. Radom Variables ad Distributios 170.. Expectatio 173.3. Quatiles, Momets ad Their Estimators

### Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find

1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.

### Chapter 5: Basic Linear Regression

Chapter 5: Basic Liear Regressio 1. Why Regressio Aalysis Has Domiated Ecoometrics By ow we have focused o formig estimates ad tests for fairly simple cases ivolvig oly oe variable at a time. But the core

### Week 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable

Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5

### TI-89, TI-92 Plus or Voyage 200 for Non-Business Statistics

Chapter 3 TI-89, TI-9 Plu or Voyage 00 for No-Buie Statitic Eterig Data Pre [APPS], elect FlahApp the pre [ENTER]. Highlight Stat/Lit Editor the pre [ENTER]. Pre [ENTER] agai to elect the mai folder. (Note:

### Actuarial Models for Valuation of Critical Illness Insurance Products

INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 9, 015 Actuarial Models for Valuatio of Critical Illess Isurace Products P. Jidrová, V. Pacáková Abstract Critical illess

### Topic 5: Confidence Intervals (Chapter 9)

Topic 5: Cofidece Iterval (Chapter 9) 1. Itroductio The two geeral area of tatitical iferece are: 1) etimatio of parameter(), ch. 9 ) hypothei tetig of parameter(), ch. 10 Let X be ome radom variable with

### Institute of Actuaries of India Subject CT1 Financial Mathematics

Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i

### COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS

COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat

### A Review and Comparison of Methods for Detecting Outliers in Univariate Data Sets

A Review ad Compariso of Methods for Detectig Outliers i Uivariate Data Sets by Sogwo Seo BS, Kyughee Uiversity, Submitted to the Graduate Faculty of Graduate School of Public Health i partial fulfillmet

### Universal coding for classes of sources

Coexios module: m46228 Uiversal codig for classes of sources Dever Greee This work is produced by The Coexios Project ad licesed uder the Creative Commos Attributio Licese We have discussed several parametric