Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.3 / 7.120
Week 7 Announcement
We are in the process of marking your
mid-term
exams. You
will get your marks soon.
The
assignment
(15%) (a.k.a., the Stats Project) will be made
available athe end this week (Week 7), two weeks before it is
due for submission. This activity will require the use of RStudio.
The Week 7 online tutorial is due Sunday, 6pm.
Chapter 7
:
Statistical Inference: Hypothesis Testing & Central Limit Theorem
MATH1041:
Page 782 / 898

Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.4 / 7.120
The Agenda Slide
Overarching aim of the course:
introducing Statistics, the study
of collecting, analysing and interpreting data (fundamental to any
quantitative research)
First class of Week 7
Last time:
Confidence intervals
The
t
-distribution
Today:
Hypothesis tests for
μ
, and introducing
p
-values
The Central Limit Theorem
Chapter 7
:
Statistical Inference: Hypothesis Testing & Central Limit Theorem
MATH1041:
Page 783 / 898

Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.5 / 7.120
Confidence Intervals Revision
TRUE or FALSE?
1
If you have a 95% confidence interval
[
100.5, 110.2
]
for the true
mean, there is a 95% probability that the true mean value is
between 100.5 and 110.2.
2
It is better to have a narrow (shorter) confidence interval than
a wide one, as it gives us more
certain
information (if the same
confidence level is used each time).
3
If your study involves twenty 95% confidence intervals, then you
expect
about
one to not contain
μ
.
Chapter 7
:
Statistical Inference: Hypothesis Testing & Central Limit Theorem
MATH1041:
Page 784 / 898

Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.6 / 7.120
Lecture 1 Learning Outcomes
[
Ch7-L1-O1
]
Understand the reasoning of hypothesis testing
[
Ch7-L1-O2
]
Understand what
p
-values are and their limitations
By the end of this lecture you should be able to:
perform tests about the mean
μ
interpret correctly the results of a test procedure
Chapter 7
:
Statistical Inference: Hypothesis Testing & Central Limit Theorem
MATH1041:
Page 785 / 898

Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.7 / 7.120
Introduction
•
So far we have used statistics to
estimate an unknown parameter
(
e.g.
, the mean or the standard deviation), and we have learnt how to
construct an interval where we believe the true parameter lies (with
some high level of confidence).
•
Now, suppose we claim that our unknown parameter (
e.g.
, the
mean
μ
of some random variable of interest) belongs to some set of
hypothesized values. These hypothesized values will depend on the
research question. So now
we would like to prove that our claim
is true
.
Chapter 7
:
Statistical Inference: Hypothesis Testing & Central Limit Theorem
MATH1041:
Page 786 / 898

Lecture 1: Hypothesis Tests for
μ
, and Introducing
P
-values
Slide 7.8 / 7.120
Introduction
Example 7.49
Suppose we make a claim that next year, students will sleep less than
this current year.

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