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One of the earliest applications of the Poisson

Mathematical Statistics and Data Analysis | 3rd Edition | ISBN: 9788131519547 | Authors: John A. Rice ISBN: 9788131519547 224

Solution for problem 3 Chapter 8

Mathematical Statistics and Data Analysis | 3rd Edition

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Mathematical Statistics and Data Analysis | 3rd Edition | ISBN: 9788131519547 | Authors: John A. Rice

Mathematical Statistics and Data Analysis | 3rd Edition

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Problem 3

One of the earliest applications of the Poisson distribution was made by Student (1907) in studying errors made in counting yeast cells or blood corpuscles with a haemacytometer. In this study, yeast cells were killed and mixed with water and gelatin; the mixture was then spread on a glass and allowed to cool. Four different concentrations were used. Counts were made on 400 squares, and the data are summarized in the following table: Number Concentration Concentration Concentration Concentration of Cells 1 2 3 4 0 213 103 75 0 1 128 143 103 20 2 37 98 121 43 3 18 42 54 53 4 3 8 30 86 5 1 4 13 70 6 0 2 2 54 7 0 0 1 37 8 0 0 0 18 9 0 0 1 10 10 0 0 0 5 11 0 0 0 2 12 0 0 0 2 a. Estimate the parameter for each of the four sets of data. b. Find an approximate 95% confidence interval for each estimate. c. Compare observed and expected counts.

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Psychological Testing Chapters 1 -4 Study Guide Know the following: Psychological tests- a device or procedure designed to measure variables related to psychology- involves analysis of a sample of behavior Psychometric soundness- accurately of a psychological test Psychometrics- defined as the science of psychological measurements Testing-the process of measuring psychology- related variables by means of devices or procedures designed to obtain a sample of behavior. Assessment- the gathering and integration of psychological related data for the purpose of making a psychological evaluation that is accomplished through the use of tools such as tests, interviews, case studies, behavioral occurrences and specially designed apparatuses and measurement procedures Role play- improvised or partially improvised part in a simulated situation Portfolio analysis- analysis of work files made of media such as paper, canvas, film, video, audio or other media. Case history- records transcripts and other accounts in written pictorial or other form that preserve archival information, official and informal accounts and other forms that preserve archival information. (Includes files from schools, hospitals, employers, religious institutions, and criminal justice agencies) Behavioral observation- monitoring the actions of others or oneself by visual or electronic means while recording quantitative and/or qualitative information regarding the actions Interview verbal and non-verbal aspects are recorded One interviewer asks questions while many record. Groupthink Scales of Measurement – nominal, ordinal, ratio, and interval Have one or more distinguishing classification or categorization based into mutually exclusive and nominal scale (p. 74) exhaustive categories. ordinal scale (p.74) permit classification, rank order has a true zero point and can use mathematical ratio scale (p. 76) operations Interval scale- Frequency distributions – grouped frequency distributions, histogram, bar graph Test-score intervals can be used to replace the actual grouped frequency distribution (p.79) test scores. is a graph with vertical lines drawn at the true limits histogram (p. 80) of of each test score. Measures of central tendency – mean, median, mode mean (p.80) average (sum of observation divided by total.) median (p.84) the middle score in a distribution mode (p. 85) the most frequently occurring score in a distribution. Correlation coefficient is the number that probides us with an index of the coefficient of correlation (p.124) strength of the relationship between two things. States- "distinguish one person from another but are states (p.101) relatively less enduring" Traits- "any distinguishable relatively enduring way in which trait (p. 101) one individual varies from another" Construct- "An informed, scientific concept developed to construct (p. 102) describe or explain behavior." Reliability- is the test consistent Validity- does the test measure what it is supposed to measure Criterion-referenced testing- "Method of evaluation and way of deriving meaning criterion- referenced testing and from test scores by evaluating an individual's score assessment with reference to set standard." Clinical Interview- Ethics in psychological testing- a body of principles of right proper or good conduct. Standards for Psychological and Educational Tests- covers issues related to test construction evaluation administration and use. And special applications to linguistic minorities. Legal cases (e.g., Mitchell v. State, Tarasoff) The Family Rights and Privacy Act Projective tests- a test where an individual is asked to project onto an ambiguous stimulus his or her feelings. Bell curves – normal distribution, negative skew, positive skew, quartiles, standard deviations, relation to measures of central tendency, stanines, z- scores, T-scores, percentiles (review the handout) Conversion of raw scores to standard scores- a corresponding scales which has been made to fit raw data to the bell curve- Correlations- The mean of all possible split half correlations coefficient alpha (149) corrected by Spearman-Brown formula. the degree of relationship between forms of a test can be evaluated by means of an alternative -forms coefficient of equivalence (144) or parallel forms confident of reliability represents the influence of particular facets on the coefficient of generalizability (158) generalizability test score The method of determining the degree of consistency coefficient of inter-scorer reliability among scores by calculating the correlation (151) coefficient. Is what test retest reliability is called when the period coefficient of stability ( between tests is greater than six months. Self-report personality tests- can be a problem if the subject doesn’t answer true fully. Identify the key people, assessments, and or events that influenced the history and use of psychological tests along with significance and/or contributions. CAPA- computer assisted psychological assessment Barbara c Pavlo- uses interviews, Beck’s test for depression and anxiety School ability tests Achievement tests- accomplishments or degree of learning Diagnostic test- refers to a tool of ruling out alternative conclusions Informational evaluation- as a typical nonsystematic assessment that leads to the formation of an opinion or attitude Oscar Krisen Buros- created the mental measurement yearbook a consumer report for tests. Galton worked on heredity Wilhelm Wundt founded the first experimental psychology lab at Leipzig James Cattell worked on reaction time Victor Herni measurement of abilities of memory and social comprehension Goddard- got binet’s intelligent tests adopted in multiple contexts and on Ellis island learned that cultural specific tests Dr. Diane Jeffery- a psychometric professor Minimum competency testing- formal testing programs designed to be used in decisions regarding various aspects of student education Truth in testing legislation allowed test takers to learn the means by which they are being judged PARC v. Commonwealth of Pennsylvania- Pennsylvania association for retarded children brought suit because mentally retarded children were denied public education In Mills v board of Education of District of Columbia Commonwealth of Pennsylvanian- suit on behalf of children with behavioral and emotional and learning impairments Daubert v Merrell Dow Pharmaceuticals- prescription drug bendectin to relieve nausea during pregnancy lead to birth defects. Charles Spearman developed the Spearman Rho

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Textbook: Mathematical Statistics and Data Analysis
Edition: 3
Author: John A. Rice
ISBN: 9788131519547

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One of the earliest applications of the Poisson