Today, we will explore the intriguing intersection of artificial intelligence and statistics. This guide aims to assist in selecting the most suitable statistical test for hypothesis testing.

What is sample and population mean?

It’s essential to grasp the concepts of sample and population in statistics, as they form the foundation of statistical analysis. Here’s a clear breakdown:

The relationship between sample and population is critical for valid statistical analysis.

1.1 What is sampling? Why do we need sampling ?

Sampling is practical when studying an entire population is impractical or impossible. It saves time and resources while still providing valuable insights.

1.2 Why is Data Representation important in statistics?

A well-chosen sample accurately reflects the population’s characteristics.

If the sample is biased, the conclusions drawn may not be valid.

Understanding the distinction between sample and population helps analysts conduct research effectively. Mastering these concepts is crucial for any student or analyst looking to thrive in the field of statistics.

For example, when the population :

• Variance (σ²) is known.

• The sample size is less than 30.

• and the population follows a normal distribution.

Therefore, hypothesis testing for the population mean can be conducted using a z-test or a t-test.

However, the example above is only one of the scenarios of the sample and population conditions.

You may perceive this as somewhat complex, but it truly isn't. Today, we will simplify the system and utilize examples to gain a deeper understanding and master the most crucial aspect of inferential statistics: hypothesis testing.

2.How do you select a test statistic in hypothesis testing? With four criteria

Assessing sample and population scenarios involves four key criteria:

1. Population Variance: Determine if the population variance (σ²) is known.

2. Homogeneity of Variances: Check if the population variances are equal (σ₁² = σ₂²).

3. Normal Distribution: Evaluate whether the populations follow a normal distribution (N(μ, σ²)).

4. Sample Size: Assess if the sample size (n) exceeds 30, distinguishing between large (n > 30) and small samples (n ≤ 30).

This structured approach ensures all critical aspects are addressed efficiently.

3.Hypothesis testing for proportions formula

By evaluating these four criteria, we can determine which hypothesis test to use for inferring the estimated parameter of population means. The distributions and their formulas under different conditions are summarized as follows:

In the following templates, we will illustrate the three types of scenarios to deepen our understanding of the parameter hypothesis test for the population mean.

Stay tuned for our upcoming demonstrations to explore more fascinating data visualization and statistics tutorials in an easy way to utilize vivid examples .

Using the AI Agent online tool, Bayeslab, anyone can organize, analyze, plot data charts, and make business data predictions like a professional data analyst based on previous data.

About Bayeslab

• Bayeslab: Website

The AI First Data Workbench

• X: @BayeslabAI

• Documents: https://bayeslab.gitbook.io/docs

• Blogs:https://bayeslab.ai/blog

Bayeslab is a powerful web-based AI code editor and data analysis assistant designed to cater to a diverse group of users, including :

👥 data analysts ，🧑🏼‍🔬experimental scientists, 📊statisticians, 👨🏿‍💻 business analysts, 👩‍🎓university students, 🖍️academic writers, 👩🏽‍🏫scholars, and ⌨️ Python learners.