MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 6 - Solutions
1.
(i) Assuming that each passenger has the same probability of showing up,
and each passenger shows up or not independently of all other passengers,
then Y Bi(n, p) with

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 2 - Solutions
1. Only method (iii) is likely to lead to a representative sample. All the other
methods are likely only to sample a restricted part of the population and lead
to bias.
2

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 9 - Solutions
1. A sample of n = 81 students took a test. In the sample of scores, x
= 74.6
and s = 11.3. Note that here is unknown. We are not told that the data
are normally distrib

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 4
Attempt the calculations for these questions by hand, using a calculator at most.
When estimating the 100% quantile of a distribution, you should use the methodology based on the val

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 10 - Solutions
1.
(i) The width of the 100(1)% CI is given by the difference of the end-points,
2z/2 s.e.(
c p). For fixed , this is proportional to s.e.(
c p).
0.00
0.05
0.10
v( p )
0

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 10
1. Let X1 , . . . , Xn be a random sample of from Bi(1, p), where the value of p is
unknown. The approximate 100(1 )% confidence intervals for p discussed in
lectures were of the fo

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 2
1. A by-election is due to be held next week in a particular town. By polling a
sample of the voting population we want to try to predict which of the Labour,
Conservative, Liberal D

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 6
1. Based on long experience, an airline has found that on average 6% of people
who have bought tickets for a flight on a particular route do not show up for the
flight. (Some may be

MATH10282 Introduction to Statistics
Semester 2, 2015/16
Example Sheet 9
1. A random sample of n = 81 students took an achievement test and had their
scores recorded. The sample mean of the scores was found to be 74.6 and the
sample standard deviation was

MATH10282 Introduction to Statistics
Chapter 3 - Probability models for data
Tim Waite
School of Mathematics
University of Manchester
[email protected]
11 February, 2016
Introduction
Continuous data
Discrete data
Approximations
Chapter 3 - Pr

MATH10282 Introduction to Statistics
Chapter 2 - Representing sample data
Tim Waite
School of Mathematics
University of Manchester
[email protected]
4 February, 2016
Introduction
Numerical summaries
Graphical summaries
Discussion
Chapter 2: R

7
Confidence intervals
7.1
Interval estimation
So far in this module, whenever we have fitted a probability model to a data set,
we have done so by calculating point estimates of the values of any unknown
parameters . However, it is very rare for a point

MATH10282 Introduction to Statistics
Introduction & Chapter 1
Tim Waite
School of Mathematics
University of Manchester
[email protected]
2 Feb 2016
Course introduction
Populations and samples
Finite population sampling
Sampling from a general

MATH10282 Introduction to Statistics
Chapter 7: Confidence Intervals
Part I - Single sample procedures
Tim Waite
School of Mathematics
University of Manchester
[email protected]
10 March 2016
Introduction
CI for a mean
CI for a proportion
CI

5
Point estimation
5.1
Introduction
The objective of a statistical analysis is to make inferences about a population
based on a sample. Usually we begin by assuming that the data were generated
by a probability model for the population. Such a model will

6
Likelihood for discrete data
6.1
The likelihood function
The parameter estimators we have considered so far have mostly been motivated
is an intuitive estimator of the
by intuition. For example, the sample mean X
population mean. However in many situat

MATH10282 Introduction to Statistics
Chapter 9: Hypothesis testing (Part II)
Single sample procedures
Tim Waite
School of Mathematics
University of Manchester
[email protected]
April 2016
Normal mean, 2 known
Normal mean, 2 unknown
Non-normal

MATH10282 Introduction to Statistics
Chapter 4 - Sampling distributions of sample statistics
Tim Waite
School of Mathematics
University of Manchester
[email protected]
18 February, 2016
Introduction
Sample mean
Sample proportion
Sample varian

9
Hypothesis testing (Part 2)
Single sample procedures
9.1
Introduction
In this chapter we will discuss specific applications of hypothesis testing where
we have a single sample of data and wish to test hypotheses regarding the value
of a population mean

MATH10282 Introduction to Statistics
Chapter 10: Hypothesis testing (Part III)
Procedures for two independent samples
Tim Waite
School of Mathematics
University of Manchester
[email protected]
April 2016
Introduction
Normal dists., 12 , 22 kn

10
Hypothesis testing (Part 3)
Procedures for two independent samples
10.1
Introduction
In this chapter we will extend hypothesis testing to the scenario in which there
are two independent samples of data, and the aim is to make an inference about
the dif

7.3
Procedures for two independent random samples
In this section we will look at procedures for when we have two independent
random samples available, both of which can be used to estimate the value of
the same parameter in the two populations. The aim w

MATH10282 Introduction to Statistics
Chapter 7: Confidence Intervals
Part 2 - Two sample procedures
Tim Waite
School of Mathematics
University of Manchester
[email protected]
9 March 2016
Procedures for two independent random samples.
We will

MATH10282 Introduction to Statistics
Chapter 5 - Point estimation
Tim Waite
School of Mathematics
University of Manchester
[email protected]
26 February, 2016
Introduction
The main aim of a statistical analysis is to make inferences about
the

MATH10282 Introduction to Statistics
Chapter 6 - The likelihood function (for discrete data)
Tim Waite
School of Mathematics
University of Manchester
[email protected]
6 March 2016
Introduction
I
Parameter estimation is a very important topic

8
Hypothesis testing (Part I)
8.1
Introduction
As we have discussed earlier in the module, one of the main aims of a statistical
analysis is to make inferences about the unknown values of population parameters based on a sample of data from the population

MATH10282 Introduction to Statistics
Chapter 8 - Hypothesis testing
Tim Waite
School of Mathematics
University of Manchester
[email protected]
April 2016
Introduction
I
So far we have looked at both point and interval estimation of
the values