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CHAPTER 5: SAMPLING DISTRIBUTION CHAPTER OUTLINE: 5.1 INTRODUCTION 5.2 SAMPLING METHODS (ONLINE VIDEO) 5.2.1 SIMPLE RANDOM SAMPLING 5.2.2 SYSTEMATIC RANDOM SAMPLING 5.2.3 STRATIFIED RANDOM SAMPLING 5.3 DISTRIBUTION OF SAMPLE MEAN 5.4 SAMPLING DISTRIBUTION OF SAMPLE MEANS - Sampling distributions of means for a NORMAL population - Sampling distributions of means for ANY population - CENTRAL LIMIT THEOREM 5.5 DISTRIBUTION OF SAMPLE PROPORTION csc/sta2208/jun2020 sta2208 / Chap 5 / Page 1 of 18
CHAPTER 5: SAMPLING DISTRIBUTION AND CENTRAL LIMIT THEOREM 5.1 INTRODUCTION Parameter is a numerical measurement describing characteristic of a population. Statistic is a numerical measurement describing characteristic of a sample. Example : The lecturers of a private college would like to investigate the amount of time its student spent in studying per week. The amount of time spent is the specific characteristic and the population consists of all the students of the college. If the mean amount spent in studying of all the students is 10 hours, then the mean value 10 hours is the population parameter. However, if the study was done on only a group of 50 students with a mean amount of 9.5 hours, then the 9.5 hours is a sample statistic. Inferential statistic permits us to draw conclusions about a population parameter based on a sample that is quite small in comparison to the size of population. There are a few basic steps that should be followed in designing a study on the population parameter: (i) Identify the objectives of the study. (ii) Collect sample data (iii)Analyze the data using statistical analysis and form conclusions. The validity of the results of statistical analysis depends on the reliability and accuracy of the data used. Sources of data: (a) Published data – produced by government agencies and private organizations, available in printed form, data tapes or on Internet services. (b) Observational study – a study conducted to observe and record the information needed, without attempting to control any of the factors that might influence the variable of interest. (c) Experimental study – a study conducted in such way where the analyst can control the factors that might affect the variable of interest. Data / information can be collected by means of survey. There are two types of survey: (a) Census EVERY member of the population is surveyed. Suitable if the size of the population is small. csc/sta2208/jun2020 sta2208 / Chap 5 / Page 2 of 18
(b) Sample survey A survey cover less than 100% of the population. Sample survey is preferable as it can save cost, time and manpower in collecting the information needed. A survey can be done by means of (a) Personal interview (b) Telephone interview (c) Self-administered questionnaire Sampling is the process of taking sample from population.

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