Chapter 4 Bivariate Data

Bivariate Data

Learning Objectives:

• understand the concept of least squares, regression lines 

and correlation in the context of a scatter diagram;

• calculate, both from simple raw data and from summarised 

data, the equations of regression lines and the product 

moment correlation coefficient, and appreciate the 

distinction between the regression line of y on x and that 

of x on y ;

• recall and use the facts that both regression lines pass 

through the mean centre and that the product 

moment correlation coefficient r and the regression 

coefficients b1, b2 are related by r ^2 = b1×b2;

• select and use, in the context of a problem, the appropriate 

regression line to estimate a value, and understand the 

uncertainties associated with such estimations;

• relate, in simple terms, the value of the product moment 

correlation coefficient to the appearance of the scatter 

diagram, with particular reference to the interpretation of 

cases where the value of the product moment correlation 

coefficient is close to +1, −1 or 0;

• carry out a hypothesis test based on the product moment 

correlation coefficient.

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Chapter 3 Chi Squared Tests

Chi Squared Tests

Learning Objectives:

• fit a theoretical distribution, as prescribed by a given 

hypothesis, to given data (questions will not involve 

lengthy calculations);

• use a χ2

-test, with the appropriate number of degrees 

of freedom, to carry out the corresponding goodness 

of fit analysis (classes should be combined so that each 

expected frequency is at least 5);

• use a χ2

-test, with the appropriate number of degrees of 

freedom, for independence in a contingency table (Yates’ 

correction is not required, but classes should be combined 

so that the expected frequency in each cell is at least 5). 

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Chapter 2 Inference using normal and t-distribution

Inference using normal and t-distribution

Learning Objectives:

• formulate hypotheses and apply a hypothesis test 

concerning the population mean using a small sample 

drawn from a normal population of unknown variance, 

using a t-test;

• calculate a pooled estimate of a population variance 

from two samples (calculations based on either raw or 

summarised data may be required);

• formulate hypotheses concerning the difference of 

population means, and apply, as appropriate:

– a 2-sample t-test,

– a paired sample t-test,

– a test using a normal distribution,

(the ability to select the test appropriate to the 

circumstances of a problem is expected);

• determine a confidence interval for a population mean, 

based on a small sample from a normal population with 

unknown variance, using a t-distribution;

• determine a confidence interval for a difference of 

population means, using a t-distribution, or a normal 

distribution, as appropriate.

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Chapter 1 Further Work on Distributions

Further Work on Distributions

Learning Objectives
• use the definition of the distribution function as a
probability to deduce the form of a distribution function in
simple cases, e.g. to find the distribution function for Y,
where Y = X^3
 and X has a given distribution;
• understand conditions under which a geometric
distribution or negative exponential distribution may be a
suitable probability model;
• recall and use the formula for the calculation of geometric
or negative exponential probabilities;
• recall and use the means and variances of a geometric
distribution and negative exponential distribution.




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Introduction

Hello.
Notes for Cambridge Alevels Further Maths (Statistics)
Statistics is in Paper 2 along with Mechanics. Paper 1 is of Pure Mathematics.Both the papers are of 100 marks and the time available is 3 hours. Both paper consist of about 11 questions with a choice in the final question. For Paper 2 the final question has teo alternatives: one from mechanics and one from statistics. Only one of these has to be attempted.
Chapters in Statistics
- Further Work on Distributions
- Inference using Normal and t distributions
- Chi Squared (χ^2) Tests
- Bivariate Data
Notes on these chapters shall be posted.