How to calculate One Tail and Two Tail Tests For Hypothesis Testing.

Summary

This 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.