1. Previous Review
Welcome back to the AI Bayeslab, Statistics series. We will demonstrate the simplest way to build a statistical knowledge base and perform flawlessly with AI interaction.
We have previously shared a range of statistical requisition knowledge and illustrated all the essential methodologies with suitable AI visualization examples.
Let's move forward with a hypothesis test for two population means.
Once you grasp this, you could apply it to so many helpful life and work analysis cases, such as:
- If there is a noticeable salary disparity among various sexual groups
- After dedicating significant effort over several months, you may want to assess whether your sports performance has improved. If it has, that indicates your training method is on the right track, correct?
- Evaluating whether a new drug is more effective than an existing one for treating a particular condition.
- Determining if there is a significant difference in customer satisfaction ratings between two products.
- Assessing whether implementing a new teaching method has improved student test scores compared to the traditional method.
- Comparing the average time spent on different tasks by employees to optimize workflow and improve productivity.
- Investigate if a new marketing strategy leads to higher sales than the previous strategy.
- Assess if the new product design has markedly improved before committing substantial resources to marketing promotions.
This method can be applied to countless situations, helping you make more rational decisions about shopping or pivotal career moments.
You will enjoy exploring and utilizing this remarkable statistical technique today. Let's start right now.
Example1_Description of Data(σ² Known):
Two Groups Data Description: Score Differences Based on Gender
The population of both groups adheres to a Normality Curve distribution.
Group 1: Males, sample size =25, with a population variance of 64 for grades.
Group 2: Females, sample size = 16, with a population variance of 49 for grades. The sample mean for Group 1 is 104, while Group 2's is 102.Question: At the 5% significance level, is there a significant difference in scores between males and females?
Step1. State the Hypothesis
- Null Hypothesis (H₀): Typically represents no significant difference or effect. For example,
- Alternative Hypothesis (H₁): Indicates a significant difference or effect.
We apply a two-tailed test in this situation, contrasting the Null Hypothesis (H₀) with the Alternative Hypothesis (H₁).
H₀: μ₁ = μ₂ or μ₁-μ₂= 0
H₁: μ₁ ≠ μ₂ or μ₁-μ₂≠ 0
Step2. Choose the Significance Level and Appropriate Test
The population variances are both known and adhere to a normal distribution curve.
To refresh our memory, we established four criteria that guide the selection of an appropriate hypothesis test. We created a summary sheet to evaluate both the sample and the population, which helped us select the test statistic and the corresponding formula.
In this scenario, we can utilize the Z distribution and the test statistic detailed below:
Step3. Calculate the Test Statistic
We have calculated the means of the two samples above:
▶︎ Female: X̅₁ = 101.814
▶︎ Male: X̅₂ = 103.801
We can calculate the corresponding Z value by substituting these into the formula.
(x̄₁ - x̄₂)
Z = _____________________
√(σ₁²/𝑛₁ + σ₂²/𝑛₂)
However, at this point, we will not perform the calculation manually. We will integrate it into one step and let the AI Agent perform the calculation based on a selected formula and the null hypothesis.
Step4. Make a Decision
The final AI Result：
- Calculated Z value: -0.8435
- Critical Z value at 5% significance level: ±1.9600
- Decision: Fail to reject the null hypothesis: There is no significant difference in scores between males and females.
AI prompts are powerful tools that enable us to accomplish various tasks and obtain desired results efficiently. By leveraging technology this way, I believe we have an incredible opportunity to reintegrate statistics into people's daily routines, rekindling interest in data and analytical thinking.
This revival is essential because statistics can provide valuable insights into various aspects of life, helping individuals make more informed decisions.
By making statistics accessible and relevant, we enhance understanding and empower people to engage with data meaningfully, ultimately enriching their everyday experiences.
Stay tuned, subscribe toBayeslab, and help everyone gain mastery in the wisdom of statistics affordably.