Chapter 13
The Accuracy of Averages
13.1 Estimators and estimates
As its name suggests, the aim of estimation is to determine the approximate value of the population parameter on the basis of a sample statistic, which is the essence of statistical inferen
Ch
11
ChanceErrorsinSampling
Ahealthstudyisdoneonarepresentativecrosssectionof 4,738adults Theresearchercansampleonly100ofthem Ourquestioniswhetherthesampleisrepresentative? Assumethepopulationhad3,032(64%)male Thenwemightpick
F F MF M MMMF M MF MMF F MMF
Chapter 1
What is Statistics?
1.1 Introduction
Simply put, statistics is a way of getting information from data. Data can be regarded as facts, and we shall especially be concerned with numerical facts, collected together for reference or information. Inf
Chapter 2
The Graphical Representation of Data
2.1 The Histogram
Todays world has been described as the information age, and one of its peculiar characteristics is the abundance of data. Data in their raw form can be dicult to comprehend. One useful way t
Chapter 3
Numerical Descriptive Techniques
Descriptive statistics consists not only of graphical summaries, but also numerical methods. Since we have introduced the histogram in the last chapter, the most important graphical summary of data, in this chapt
Chapter 4
A First Look at Bivariate Data
4.1 Graphical representation
So far we have looked at a single variable or what is known as univariate data and their descriptive and numerical summaries. We now turn to bivariate data, that is statistics with two
Chapter 5
Controlled Experiments and Observational Studies
It is useful to distinguish between controlled experiments and observational studies. In many experiments, for example, often an investigator wishes to know the eect of a treatment (like a vaccine
Chapter 6
The Normal Distribution
The Gaussian distribution, which we have mentioned a number of times already, is perhaps the most common and most important of the continuous distributions treated in statistics. The real reason for the importance of the
Chapter 7
Elementary Probability
In this chapter we will introduce the basics of probability needed to understand statistical concepts and ideas. The literature identies three denitions of probability; 1) the classical denition, 2) the empirical or freque
Chapter 8
Discrete Probability Distributions
We begin by dening a random variable. A random variable is a function or rule that assigns a number to each outcome of an experiment. Instead of talking about the coin ipping event as heads, tails, for example.
Chapter 9
Continuous Probability Distributions
In contrast to a discrete random variable, a continuous random variable is one that can assume an uncountable number of values, i.e we cannot list the possible values because there is an innite number of them
Chapter 10
The Expected Value and Standard Error
This chapter introduces us to the very important concepts of random processes and their sampling distributions. To keep ideas manageable, it is best motivated by way of example.
10.1
Expected value
Assume 1
Chapter 11
Chance Errors in Samples
11.1 Percentages
A health study is done on a representative cross section of 4,738 adults. The researcher can sample, say, only 100 of them. Our question is whether the sample is representative? Assume the population ha
Pr act i ce Quest i ons
Pr obabi l i t y
#1
( A) 1 2 3 ( B) 1 2 3 4
One t i cket wi l l be dr awn f t he boxes shown above: Fi nd t he chances t hat : ber dr awn f r om ( a) The num t han t he one f r om B. ber dr awn f r om ( b) The num t he one f r om
Chapter 14
Test of Signicance
In this chapter we put together the few skills and techniques we have learnt so far into a formal method for testing hypothesis, which is the classical way of doing statistical inference. Assume that as a new employee at the
Try these
Please do not distribute
#1
The number of errors, X, on each page of a 200 pages book was monitored. The results when summarized showed that: X = 920 and X2 = 5032 Calculate the mean and the SD of the number of errors per page.
#2
A travel age
Revision for Mid-term
(Please do not distribute) Q estion u Of all the households in the U 40 have a plas a T and 50 K, % mV % have a laptop co p m uter. There are 25 of households that have % both a plas a T and a laptop. Find the probabil i ty that a mV