Applied Economics & Statistics: Topic 6 - Hypothesis Testing*

Question 1

Define ‘hypothesis’

Answer 1

A statement about the value of a population parameter that is subject to
verification.

Question 2

What’s the name for ‘a statement about the value of a population parameter that is subject to
verification’?

Answer 2

Hypothesis

Question 3

Define ‘hypothesis testing’

Answer 3

A procedure based on sample evidence and probability theory to determine
whether the hypothesis is a reasonable statement

Question 4

What’s the name for ‘a procedure based on sample evidence and probability theory to determine
whether the hypothesis is a reasonable statement’?

Answer 4

Hypothesis Testing

Question 5

What’s ‘one sample testing’?

Answer 5

Testing one sample against its population Examples: Are the grades of A-level students in Birmingham significantly
different from the grades of the entire A-level student population in
England? Is the growth rate of Asian economies significantly different from
the growth rate of the entire world?

Question 6

What’s ‘2 sample testing’?

Answer 6

Testing 2 samples in the same population against each other Examples: Are the grades of A-level students in Birmingham significantly
different from the grades of A-level students in London? Is the growth rate
of Asian economies significantly different from the growth rate of
European economies?

Question 7

What are the 3 assumptions that have to be satisfied to conduct one sample hypothesis testing?

Answer 7

• Random sampling is employed.
• Level of measurement is interval or ratio (we need to calculate the
  mean).
• Sampling distribution is normal (we can be sure of this if the sample size is large enough, as per the Central Limit Theorem).

Question 8

Describe & explain a null and alternate hypothesis

Include symbols

Answer 8

Null Hypothesis (H0): A statement about the value of a population parameter
Alternate hypothesis (H1): A statement that is accepted if the null
hypothesis is false
- Equalities are always part of the null: =, ≤, ≥.
- Inequalities are always part of the alternate:̸=, <, >.
- H0 is presumed to be true, and H1 bears the burden of proof. So we
assume the null is true until the sample evidence is sufficiently strong
to suggest otherwise. For example, we assume someone on trial is
innocent until proven guilty beyond reasonable doubt
- Possible null and alternate hypothesis symbols:
H0 H1
= /= 2-tailed
≥ < 1-tailed
≤ > 1-tailed
H0 usually represents a situation of no change or no difference. The
alternate hypothesis will always counter this: both H0 and H1 cannot be
true
- A null hypothesis is a statistical tool that helps frame questions in a
consistent way. It is not the same thing as your research hypothesis.
Example:
Research hypothesis: Edgbaston is an affluent area, so it is probable
that households take a significantly higher number of holidays a year
than Birmingham households overall.
Null hypothesis: There is no statistically significant difference
between holidays taken by Edgbaston households and Birmingham
households overall.

Question 9

What’s the aim of hypothesis testing?

Answer 9

To decide between the null and the alternate hypotheses

Question 10

What’s an important note to remember when it comes to WORDING in conclusions of hypothesis tests?

Answer 10

Important note: We can never prove a null is correct (never use the word
“accept” for a null hypothesis). If we cannot reject the null hypothesis at
a reasonable level of confidence, the conclusion is “fail to reject the null
hypothesis.” If we cannot reject the null it does not necessarily mean that
the null is true, only that there is not sufficient evidence to reject it

Question 11

State the steps of a one sample hypothesis test

Answer 11

1. State the null and alternate hypothesis
2. Select a level of significance. We tend to choose α = 0.05 (synonymous with choosing a 95% confidence level when calculating a confidence interval).
3. Select the test statistic
4. Formulate the decision rule

Question 12

What’s a ‘test statistic’?

Answer 12

A value, determined from sample information, used to determine whether
to reject the null hypothesis

Question 13

What’s the name for ‘a value, determined from sample information, used to determine whether
to reject the null hypothesis’?

Answer 13

A test statistic

Question 14

Describe & explain how we decide which test distribution to use in a ‘one-sample hypothesis test’

Answer 14

• The distribution of the statistic is known to us and this means that
  we can determine whether the value of the test statistic is large (in
  the tails of the distribution) or small (not in the tails).
• This helps us to decide whether the null hypothesis is valid or not.
  If the population standard deviation, σ, is known, we use the standard
  normal (z) distribution.
• If the population standard deviation, σ, is unknown, but the sample is
  large, s is used to substitute for σ, but we still use the standard
  normal (z) distribution.
• If the population standard deviation, σ, is unknown, and the sample is
  small, we use the t-distribution.

Question 15

What does ‘formulating the decision rule’ involve?

Answer 15

Determining the rejection area of the sampling distribution of
the test statistic

Question 16

Which step in hypothesis testing involves determining the rejection area of the sampling distribution of
the test statistic?

Answer 16

Formulating the decision rule

Question 17

What’s a critical value?

Answer 17

The dividing point between the region where the null hypothesis is rejected
and the region where it is not rejected