Hypothesis Testing - Null and Alternative Hypotheses
Summary
TLDRThis video script offers an introduction to hypothesis testing, focusing on formulating null and alternative hypotheses. It uses real-world examples to illustrate the process, starting with a company's calculator mass average. The script explains that the null hypothesis (H0) represents the accepted status quo, while the alternative hypothesis (Ha) is the claim that contradicts H0. Examples include testing the average mass of calculators, high school completion rates, and vehicle ownership percentages. The script emphasizes that stating hypotheses involves identifying whether the test is about a mean or a proportion, and then formulating H0 and Ha accordingly.
Takeaways
- π The video introduces the concept of hypothesis testing, focusing on how to state the null and alternative hypotheses.
- π― The null hypothesis (H0) represents the status quo or the current accepted value, which is what the majority believes to be true.
- π The alternative hypothesis (Ha) is the claim that contradicts the null hypothesis, representing what the researcher is trying to prove to disprove H0.
- β When stating hypotheses, it's important to determine whether you're dealing with a mean (average) or a proportion (percentage).
- π The symbol for the mean is 'mu' (ΞΌ), and for a proportion, it's represented as 'p'.
- π In the first example, the null hypothesis is that the average mass of calculators is 450 grams, while the alternative hypothesis is that it is different.
- π For the second example, the null hypothesis is that at least 80% of students will complete high school, and the alternative is that less than 80% will.
- π The third example involves a teacher testing if the average GPA is different from 2.7, with the null hypothesis being an average GPA of 2.7 and the alternative being different.
- π‘ In the fourth example, the null hypothesis is that no more than 75% of residents own a vehicle, with the alternative hypothesis being that more than 75% do.
- π Stating hypotheses doesn't require much complexity; it involves clearly articulating the current accepted value (null) and the contradictory claim (alternative).
Q & A
What is the purpose of the null hypothesis (H0) in hypothesis testing?
-The null hypothesis (H0) represents the status quo or the current accepted value that the majority of people hold to be true. It serves as a benchmark against which the alternative hypothesis is tested.
How is the alternative hypothesis (Ha) different from the null hypothesis (H0)?
-The alternative hypothesis (Ha) is contradictory to the null hypothesis (H0). It is what the researcher tries to prove in order to disprove the null hypothesis. If the researcher fails to disprove the null hypothesis, it is likely to be correct.
In the context of the video, what does the symbol 'mu' represent?
-In the video, the symbol 'mu' represents the mean of a dataset, specifically the average mass of the calculators in the example provided.
What is the null hypothesis for the calculator manufacturing company example?
-The null hypothesis for the calculator manufacturing company example is that the average mass of the calculators is 450 grams, which is represented as H0: ΞΌ = 450.
What is the alternative hypothesis for the calculator manufacturing company example?
-The alternative hypothesis for the calculator manufacturing company example is that the average mass of the calculators is different from 450 grams, represented as Ha: ΞΌ β 450.
Why is it important to state both the null and alternative hypotheses before conducting a hypothesis test?
-Stating both the null and alternative hypotheses before conducting a hypothesis test is important because it sets clear expectations for the research and provides a basis for making decisions about the data collected.
In the school completion rate example, what is the null hypothesis?
-In the school completion rate example, the null hypothesis is that at least 80 percent of students will complete high school, represented as H0: p β₯ 0.80.
What is the alternative hypothesis in the school completion rate example?
-The alternative hypothesis in the school completion rate example is that less than 80 percent of students will complete high school, represented as Ha: p < 0.80.
How does the video script differentiate between a hypothesis test for a mean and a proportion?
-The video script differentiates between a hypothesis test for a mean and a proportion by using the keyword 'average' for means, represented by 'mu', and 'percentage' for proportions, which are represented as 'p'.
What is the null hypothesis for the high school GPA example in the video?
-The null hypothesis for the high school GPA example is that the average GPA of students is 2.7, represented as H0: ΞΌ = 2.7.
What is the alternative hypothesis for the high school GPA example in the video?
-The alternative hypothesis for the high school GPA example is that the average GPA of students is different from 2.7, represented as Ha: ΞΌ β 2.7.
In the vehicle ownership example, what is the null hypothesis?
-In the vehicle ownership example, the null hypothesis is that the percentage of residents who own a vehicle is no more than 75 percent, represented as H0: p β€ 0.75.
What is the alternative hypothesis for the vehicle ownership example?
-The alternative hypothesis for the vehicle ownership example is that the percentage of residents who own a vehicle is greater than 75 percent, represented as Ha: p > 0.75.
Outlines
π Hypothesis Testing: Null and Alternative Hypotheses
This paragraph introduces the concept of hypothesis testing, focusing on how to state the null and alternative hypotheses. The null hypothesis (H0) represents the status quo or the accepted value, while the alternative hypothesis (Ha) is the claim that contradicts H0 and is what researchers attempt to prove to disprove H0. The example provided involves a company that manufactures calculators with an average mass of 450 grams. An engineer believes the average mass is different and conducts a test. The null hypothesis is that the average mass is 450 grams, and the alternative hypothesis is that it is not 450 grams. The paragraph explains the importance of determining whether the hypothesis is about a mean or a proportion, which is indicated by keywords like 'average' or 'percentage'.
π Hypothesis Testing Examples: Proportions and Means
This paragraph continues the discussion on hypothesis testing with two additional examples. The first example involves teachers who believe that at least 80% of students will complete high school, while a student disagrees and conducts a test. The null hypothesis is that the proportion of students completing high school is at least 80% (or 0.80 in decimal), and the alternative hypothesis is that it is less than 80%. The second example is about a teacher who wants to test if the average GPA of students is different from 2.7. The null hypothesis is that the average GPA is 2.7, and the alternative hypothesis is that it is different from 2.7. The paragraph emphasizes that stating hypotheses is straightforward once the type of data (mean or proportion) is identified.
Mindmap
Keywords
π‘Hypothesis Testing
π‘Null Hypothesis (H0)
π‘Alternative Hypothesis (Ha or H1)
π‘Mean
π‘Proportion
π‘Statistical Significance
π‘Sample
π‘Researcher's Belief
π‘Disprove
π‘Status Quo
π‘Evidence
Highlights
Introduction to hypothesis testing and stating null and alternative hypotheses.
Null hypothesis (H0) represents the status quo or accepted value.
Alternative hypothesis (Ha) is contradictory to the null hypothesis and what the researcher tries to prove.
Determining if the hypothesis test is about a mean or proportion based on keywords like 'average' or 'percentage'.
Example 1: Company XYZ's calculators have an average mass of 450 grams; the null hypothesis states this average.
Example 1: The alternative hypothesis suggests the average mass is different from 450 grams.
Example 2: Teachers believe at least 80% of students complete high school; this is the null hypothesis for a proportion.
Example 2: The alternative hypothesis for high school completion rate is less than 80%.
Example 3: A teacher tests if the average GPA is different from 2.7; the null hypothesis is that the average GPA is 2.7.
Example 3: The alternative hypothesis for the average GPA is that it is not equal to 2.7.
Example 4: The null hypothesis for vehicle ownership is no more than 75% of residents own a vehicle.
Example 4: The alternative hypothesis for vehicle ownership is that more than 75% of residents own a vehicle.
The process of stating hypotheses does not require much complexity.
The importance of disproving the null hypothesis to accept the alternative hypothesis.
The video provides a clear methodology for stating null and alternative hypotheses in hypothesis testing.
Transcripts
in this video we're going to do a brief
introduction into hypothesis testing
but specifically on how to state the
null and alternative hypotheses
so let's start with this problem number
one
company xyz
manufactures calculators with an average
mass of 450 grams
an engineer
believes that average weight to be
different
and decides to calculate the average
mass of 50 calculators
state the null and alternative
hypotheses
so let's start with the null hypothesis
the symbol
that corresponds to the null hypothesis
is
h sub zero
now the null hypothesis is basically the
status quo it's the claim
it's the current accepted value
that
the majority of people
holds to be true
now the alternative
hypothesis
is basically the contender
it's contradictory to the null
hypothesis
it has a symbol
h sub a
it's what the researcher tries to prove
in order to disprove
the null hypothesis
if he fails to disprove it that means
the null hypothesis is
likely to be correct
so now let's talk about how we can state
it
the first thing you want to determine is
if you're dealing with a mean or
proportion
here we have a keyword average mass
so we're dealing with
the mean
represented by the symbol mu
now if you hear the word percentage that
means you're dealing with a proportion
so the company
manufactures calculators with an average
mass of 450.
so
the accepted mean
of
the calculators
is an average of 450.
the researcher believes this to be
different
so he believes that the average weight
or the average mass
is not
450 grams
so that is the alternative hypothesis
for the sake of practice let's try
another example you can pause the video
and try if you want to
number two
the teachers in a school
believes that at least 80 percent of
students will complete high school
a student disagrees with this value and
decides to conduct a test
state the null and alternative
hypotheses
so let's start with a null hypothesis
the status quo
or the current accepted value
is eighty percent
or rather at least eighty percent
so the teachers in this school believe
that at least eighty percent of students
will complete high school since we're
dealing with april i mean percentage
this is going to be a proportion
so at least 80 percent means it could be
80 or more
so therefore the proportion is going to
be equal to or greater than 0.80
which is the decimal equivalent of 80
now the student disagrees with this
value
that means that the student believes
it's less than 80
it's not equal to or greater than 80
percent
so for the alternative hypothesis
p is going to be less than 0.80
and as you can see it doesn't require
too much in order to state the null and
alternative hypotheses
so
this is the answer for this problem
number three
a teacher wishes to test if the average
gpa of students
in the high school is different from 2.7
state the null and alternative
hypotheses
so what can we say regarding h o and h a
now for this one it might be better to
start with h a
this is what the researcher is trying to
prove
in this case the teacher wants to prove
that the average gpa of students is
different from 2.7
so the teacher believes that
we're dealing with a mean not a
proportion so we're going to use symbol
mu the teacher believes that the average
gpa is not 2.7
which means that the status quo or the
accepted value
is 2.7
so the null hypothesis
is that the mean is 2.7 but the
alternative hypothesis what the teacher
is trying to prove is that it's
different or not 2.7
so that's it for number three number
four
the percentage of residents who own a
vehicle
in town xyz
is no more than 75 percent
a researcher disagrees with the value
and decides to survey 100 residents
asking them
if they own a vehicle
state the null and alternative
hypotheses
so
what is the status quo here
the accepted value is
no more than 75
and we're dealing with a percentage
so the proportion of residents who own a
vehicle in this town
is no more than 75 percent so let's
think about what that means
that means it can be equal to 75 but not
greater than which means it could be
less than 75
so it's going to be less than or equal
to 0.75
or 75 as a decimal
the researcher wants to disprove this uh
this fact or
this hypothesis rather
and so he decides to survey 100
residents
so he believes
that
it is greater than 75
so i put the equal sign but it's just
greater than not equal to so p
is greater than 0.75 that is the
alternative hypothesis
that's what the researcher is trying to
prove
in order to
disprove or nullify the null hypothesis
so that's the answer for this problem
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