How to calculate One Tail and Two Tail Tests For Hypothesis Testing.
Summary
TLDRThis tutorial explains one-tailed and two-tailed hypothesis tests, using a normal bell curve to illustrate the distribution of possible events. The population mean is denoted by the Greek letter 'mu', and the sample mean can vary within a certain range. A one-tailed test with a 95% confidence level implies a 5% chance (Alpha) of the sample mean falling in the rejection region. In contrast, a two-tailed test divides Alpha by two, placing 2.5% in each tail, ensuring a 95% chance of the sample mean falling within the acceptable range. Critical values for a 95% two-tailed test are ±1.96, while for a one-tailed test, they are ±1.645. The video promises more in-depth statistical insights.
Takeaways
- 📊 The tutorial discusses one-tailed and two-tailed hypothesis tests, which are statistical methods to make inferences about a population.
- 🔵 A normal bell curve is used to represent all possible events, with the population mean (μ) at the center.
- 🌿 The sample mean (x̄) can vary and is represented within a green area on the bell curve, indicating its possible positions.
- 🎯 In a one-tailed test with a 95% confidence level, there's a 5% chance (Alpha) that the sample mean will fall in the red, or rejection, region.
- 🚫 The red area signifies the rejection region where the null hypothesis would be rejected if the sample mean falls within it.
- 🔄 For a one-tailed test, the red area can be to the right or left of the mean, depending on the direction of the hypothesis.
- 🔁 In a two-tailed test at a 95% confidence level, the 5% Alpha is split into 2.5% in each tail, providing a balanced test for deviations in either direction.
- 🔢 The critical values for a two-tailed test at 95% confidence are ±1.96 z-scores, indicating the boundaries of the rejection regions.
- 🔄 Switching back to a one-tailed test, the critical values adjust to ±1.645 z-scores, reflecting a higher probability of the sample mean being extreme in one direction.
- 📚 The tutorial serves as an introductory lesson on hypothesis testing, with more advanced statistical concepts to be explored in subsequent lessons.
Q & A
What does the bell curve represent in the context of the tutorial?
-The bell curve represents 100% of all possible events, with the population mean at the center.
What is the Greek letter used to denote the population mean?
-The Greek letter used to denote the population mean is 'mu', which looks like a 'u' but is pronounced as 'me'.
What is the notation used for the sample mean in the tutorial?
-The notation used for the sample mean in the tutorial is 'x-bar' (x̄).
What is the probability range for the sample mean in a one-tailed test with a 95% confidence level?
-In a one-tailed test with a 95% confidence level, there is a 5% chance the sample mean will show up in the red area, which is also known as Alpha.
What is Alpha in the context of hypothesis testing?
-Alpha is the probability of the sample mean showing up in the red area, which is also known as the rejection region. It can also be referred to as the P-value.
How is the red area distributed in a two-tailed test at a 95% confidence level?
-In a two-tailed test at a 95% confidence level, the red area is split equally, with 2.5% on each tail (left and right).
What is the significance of the 2.5% on each tail in a two-tailed test?
-The 2.5% on each tail represents the probability of the sample mean falling in the rejection region for a two-tailed test at a 95% confidence level.
What are the critical values for a two-tailed test at a 95% confidence level?
-The critical values for a two-tailed test at a 95% confidence level are z-scores of -1.96 on the left and +1.96 on the right.
How do the critical values change for a one-tailed test?
-For a one-tailed test, the critical value on the right is a positive 1.645, and on the left, it would be a negative 1.645.
What is the purpose of discussing one-tailed and two-tailed tests in the tutorial?
-The purpose is to introduce and explain the concepts of one-tailed and two-tailed hypothesis tests, including their setup, probabilities, and critical values.
What does the term 'rejection region' refer to in hypothesis testing?
-The 'rejection region' refers to the area of the distribution where the sample mean would lead to the rejection of the null hypothesis.
Outlines
📊 Introduction to One-Tail and Two-Tail Tests
This paragraph introduces the concepts of one-tail and two-tail tests in statistical analysis. The speaker begins by explaining the setup using a normal bell curve, which represents 100% of all possible events. The population mean, denoted by the Greek letter mu (µ), is situated at the center of the curve. The sample mean, denoted by x̄, can vary and is represented within a green area on the curve. The paragraph discusses how the sample mean can fall above or below the population mean, and the probability associated with its occurrence. The speaker then explains the one-tail test with a 95% confidence level, where there is a 5% chance (represented by the red area) that the sample mean will fall outside the green area, known as the rejection region or alpha. The concept of the P-value is also introduced. The paragraph concludes with a transition to a two-tail test, where the red area is split equally on both sides of the curve, representing a 2.5% chance in each tail. The critical values for a 95% confidence level are also mentioned, with -1.96 and 1.96 for a two-tail test, and -1.645 and 1.645 for a one-tail test.
Mindmap
Keywords
💡Normal Bell Curve
💡Population Mean (μ)
💡Sample Mean (x̄)
💡Probability
💡Alpha (α)
💡P-value
💡Rejection Region
💡One-tail Test
💡Two-tail Test
💡Confidence Level
💡Critical Values
Highlights
Introduction to one-tailed and two-tailed tests
Explanation of the normal bell curve representing 100% of all possible events
Definition of population mean (mu) and its representation on the bell curve
Description of the sample mean (x̄) and its potential positions relative to the population mean
Probability of the sample mean falling within the green area in a one-tailed test
Use of a 95% probability for the sample mean to fall within the green area
Explanation of the red area as the rejection region (Alpha) with a 5% chance
The concept of Alpha as a probability and its role in hypothesis testing
Setting up a one-tailed test with the red area to the right of the population mean
Probability of the sample mean appearing in the red area in a one-tailed test
Introduction to the two-tailed test and its 95% confidence level
Division of Alpha into two equal parts for the two-tailed test
Coverage of all observations by the green and red areas in a two-tailed test
Critical values in a two-tailed test at the 95% confidence level
Identification of critical z-scores for the two-tailed test
Return to the one-tailed test and its critical values
Conclusion and anticipation of further statistical learning
Transcripts
in this tutorial I'm going to discuss
one tail and twail
tests we set this up by drawing a normal
bell
curve and the bell curve represents 100%
of all possible
events right in the middle is the
population mean and we use the Greek
letter
mu it looks kind of like a u but we call
it
me a sample mean can be anywhere within
this green area
for sample mean I use the notation
xar the value of the sample mean can be
above the population mean it can also be
below the population
mean and there's a probability that it
will show up somewhere the sample mean
will be somewhere in this green
area with a Oneil test there's some
probability that the sample mean will be
in the green
area and I'm going to use a 95%
probability and that means there's a 5%
chance the sample mean will show up in
the red
area this red area is often known as
Alpha the Greek letter
Alpha also it can be used as the P
value it's typically called the
rejection
region the sample mean has to show up in
the red area or in the green area
because these two add up to
100% in this example I'm using a 95%
confidence and you could actually use
any level you wanted
to I can also have a one tail test with
the red area to the right of the
population
mean there's a 95% chance a randomly
selected mean will be in the green area
sample
mean there is a 5% chance it will appear
in the red area a randomly selected
sample
mean but there is a 95% chance it will
be in the green
area again the red area is often called
Alpha refer to as alpha or the P value
and we refer to it also as the rejection
region now when I create a two-tail test
at a 95% level of
confidence I will take that red
area and I'll put half of it to the
right and half of it to the
left in other words I take Alpha /
two so I take the
5% divided by two and I put
2.5% on the left side and 2.5% on the
right
side you'll also see this Alpha / two in
other statistics formulas and this is
what it's referring to
there is 2.5% on the left and
2.5% on the
right 2.5% plus
95% plus
2.5% equals 100% this means all
observations and all events are
covered there is a 95% chance the sample
mean will be in the green area a
randomly selected sample
mean there is a 2.5% chance the sample
mean will be in the bottom
tail and there's a 2.5% chance the
sample mean will be in the upper tail
right
there now at a 95% level there's
critical values and these are zc
scores negative 1.96 on the left and
positive 1.96 on the right
when I return to a one tail test the
critical value on the right is a
positive
1.645 and the critical value to the left
would be a negative
1.645 and this has just been an
introduction to one and twoa
tests and there's more to come more to
learn about stats
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