# VCU STAT 210 - Lecture2 (64 pages)

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## Lecture2

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- Pages:
- 64
- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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STAT 210 Lecture 2 Introduction and Basic Definitions August 28 2017 Practice Problems At the end of each section there are a set of Practice Problems These problems reemphasize the concepts that have been discussed in the material proceeding them You should work these problems outside of class to best prepare for the tests Solutions can be found in the back of the supplement Relevant problems are practice problems associated with that day s lecture Recommended problems are problems that test questions are likely to be similar to Practice Problems Pages 9 and 10 Relevant problems I 1 through I 5 Recommended problems I 1 I 3 and I 4 Additional Reading and Examples Read the Additional Reading and Examples on pages 6 through 8 Motivating Example It is of interest to determine what percentage of all VCU students who when asked to list three things that they enjoy doing include shopping on their list Top Hat Statistics Statistics is a science that involves the extraction of information from numerical data obtained during an experiment or from a sample It involves the design of the experiment or sampling procedure and the collection of the data the analysis of the data and making inferences statements about the population based upon information in a sample Population The entire group of individuals about which the researcher wants information Examples 1 All United States citizens 2 All male students at VCU 3 All sections of all courses taught this semester at VCU Parameter Some characteristic of the population that the researcher wants to measure Examples 1 Proportion of US citizens who voted in the 2008 Presidential election 2 Average mean height of all male students at VCU 3 Proportion of all sections of all courses taught by adjunct part time faculty Parameter Some characteristic of the population that the researcher wants to measure Parameters are typically denoted with Greek letters For example the mean of a population is denoted using the Greek letter m read mu and the proportion of successes in a population is denoted by the Greek letter p read pi What is the parameter of interest Mean m Proportion p m1 m2 Is the population standard deviation s known Yes use Z No use t Do you want a confidence interval or a test CI Test ALWAYS CHECK THE ASSUMPTIONS Sample A subset of the population that is contacted and examined to gather information Example when the population is all male VCU students a sample would be all male students in this class Statistic A descriptive measure computed from data in a sample that can be expressed or evaluated numerically Example For the sample of male students in this class one can compute the average height of these students This average height is a statistic Statistic A descriptive measure computed from data in a sample that can be expressed or evaluated numerically Statistics are typically denoted with symbols involving regular English letters For example the mean of the sample is usually denoted by X read X bar and the proportion of successes in a sample is denoted by p read phat Inference A statement about a population based on the data collected in a sample Example To estimate the average height of all male VCU students we can compute the average height of the male students in this class Example 1 Example 1 Population Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number of countries or territories in the population Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries or territories in the sample Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries in the sample c 65 Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries in the sample c 65 statistic it is the percentage of the sample that had at least one athlete win a gold medal Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries in the sample c 65 statistic it is the percentage of the sample that had at least one athlete win a gold medal d 93 Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries in the sample c 65 statistic it is the percentage of the sample that had at least one athlete win a gold medal d 93 statistic it is the percentage of the sample that enjoyed the Olympics Example 1 Population the 204 countries and territories eligible to win a medal at the Olympics Sample the 20 countries or territories that were selected for further information a 204 parameter it is the number in the population b 20 statistic it is the number of countries in the sample c 65 statistic it is the

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