Statistics and data science 188
Fundamentals of hypothesis testing
Chapter 9
Introduction
In this chapter the following will be covered:
• The principles of hypothesis testing.
• How to use hypothesis testing to test a mean or proportion.
• To evaluate the assumptions of each hypothesis testing procedure and understand the
consequences if assumptions are seriously violated.
• The pitfalls and ethical issues involved in hypothesis testing.
• How to avoid the pitfalls involved in hypothesis testing.
• .
A hypothesis:
- A claim or assertion about a population parameter
Hypothesis Testing:
- Seeking to validate a claim about a population using the sample mean
o Is an inferential method
1. State a straight forward claim about the population mean (π).
1. This claim will be referred to as the Null Hypothesis (H0)
2. State a mutually exclusive claim to the Null Hypothesis
1. This is called the Alternate Hypothesis (H1)
3. Begin with the assumption that H0 is true
4. Examine the sample statistics to see if it supports H1 or H0 better
The null hypothesis(HO):
- States the claim to be validated
- Assumes the status-quo scenario
- Represents the current belief in a situation
- May or may not be rejected
o The Null Hypothesis is never accepted
- Always regards a population parameter not a sample statistic
- Written as: (<; >; =)
o A statement:
- The average diameter of a pipe in KZN is 30cm
o In Notation:
- H0: µ = 30
The alternative hypothesis (H1):
- Is the opposition of the Null Hypothesis
- Challenges the status-quo scenario
- May or may not be proven
- It is generally the hypothesis that the researcher intends on proving
- Written as:
o A statement:
- The average diameter of a pipe in KZN is larger than 30cm
o In Notation: (<; >; b)
- H1: µ > 30
, Concepts in the testing process:
- If the sample mean is close to the stated populationmean
o H0 is not rejected
- If the sample mean is far from the stated populationmean
o H0 is rejected
- How far is far enough:
o Determine through use of the critical valuesfound
in a test statistic
Risks in decision making using hypothesis testing:
o Type I Error:
o A False Alarm
o Rejection of a true Null Hypothesis
o Only occurs when H0 is True
o The probability of a Type I error is denoted as α
- Is called the <level of significance= of the test
- Is specified by the researcher in advance
o Type II Error:
o A Missed Opportunity
o Failure to reject a false Null Hypothesis
o The probability of a Type II error is denoted as β
o Only occurs when H0 is False
o Factors that effect it:
- Increased Variance (ơ^2) : Increased Type II Probability (β)
- Decreased Sample Size (n) : Increased Type II Probability (β)
- Difference Between Hypothesis Parameter and True ValueDecreases :
Increased Type II Probability (B)
Possible hypothesis test outcomes:
Fundamentals of hypothesis testing
Chapter 9
Introduction
In this chapter the following will be covered:
• The principles of hypothesis testing.
• How to use hypothesis testing to test a mean or proportion.
• To evaluate the assumptions of each hypothesis testing procedure and understand the
consequences if assumptions are seriously violated.
• The pitfalls and ethical issues involved in hypothesis testing.
• How to avoid the pitfalls involved in hypothesis testing.
• .
A hypothesis:
- A claim or assertion about a population parameter
Hypothesis Testing:
- Seeking to validate a claim about a population using the sample mean
o Is an inferential method
1. State a straight forward claim about the population mean (π).
1. This claim will be referred to as the Null Hypothesis (H0)
2. State a mutually exclusive claim to the Null Hypothesis
1. This is called the Alternate Hypothesis (H1)
3. Begin with the assumption that H0 is true
4. Examine the sample statistics to see if it supports H1 or H0 better
The null hypothesis(HO):
- States the claim to be validated
- Assumes the status-quo scenario
- Represents the current belief in a situation
- May or may not be rejected
o The Null Hypothesis is never accepted
- Always regards a population parameter not a sample statistic
- Written as: (<; >; =)
o A statement:
- The average diameter of a pipe in KZN is 30cm
o In Notation:
- H0: µ = 30
The alternative hypothesis (H1):
- Is the opposition of the Null Hypothesis
- Challenges the status-quo scenario
- May or may not be proven
- It is generally the hypothesis that the researcher intends on proving
- Written as:
o A statement:
- The average diameter of a pipe in KZN is larger than 30cm
o In Notation: (<; >; b)
- H1: µ > 30
, Concepts in the testing process:
- If the sample mean is close to the stated populationmean
o H0 is not rejected
- If the sample mean is far from the stated populationmean
o H0 is rejected
- How far is far enough:
o Determine through use of the critical valuesfound
in a test statistic
Risks in decision making using hypothesis testing:
o Type I Error:
o A False Alarm
o Rejection of a true Null Hypothesis
o Only occurs when H0 is True
o The probability of a Type I error is denoted as α
- Is called the <level of significance= of the test
- Is specified by the researcher in advance
o Type II Error:
o A Missed Opportunity
o Failure to reject a false Null Hypothesis
o The probability of a Type II error is denoted as β
o Only occurs when H0 is False
o Factors that effect it:
- Increased Variance (ơ^2) : Increased Type II Probability (β)
- Decreased Sample Size (n) : Increased Type II Probability (β)
- Difference Between Hypothesis Parameter and True ValueDecreases :
Increased Type II Probability (B)
Possible hypothesis test outcomes:
