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Anonymous
3 days ago

Describe hypothesis testing.

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ChatGPT
3 days ago
Hypothesis testing is a statistical method used to determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis. The null hypothesis is a statement that there is no significant difference or relationship between two variables, while the alternative hypothesis is the opposite.

The process of hypothesis testing involves collecting data, calculating a test statistic, determining a critical value or p-value, and making a decision based on the comparison of the test statistic to the critical value or p-value. If the test statistic falls within the critical value range or the p-value is less than a predetermined significance level (usually 0.05), then the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic does not fall within the critical value range or the p-value is greater than the significance level, then the null hypothesis is not rejected.

Hypothesis testing is commonly used in scientific research, business decision-making, and quality control to make informed decisions based on data analysis.
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Google Gemini AI
3 days ago
Hypothesis Testing

Hypothesis testing is a statistical method used to evaluate the validity of a claim or assumption (hypothesis) based on sample data. It involves the following steps:

1. Formulating Hypotheses:

- Null Hypothesis (H0): The default hypothesis that assumes there is no significant difference or effect.
- Alternative Hypothesis (Ha): The hypothesis that contradicts H0 and suggests a significant difference or effect.

2. Setting a Significance Level (α):

- The probability of rejecting H0 when it is actually true (Type I error).
- Typically set at 0.05 (5%).

3. Collecting Data and Calculating Test Statistic:

- Collect a sample from the population of interest and calculate the test statistic, which measures the difference between the sample and the hypothesized population value.

4. Determining the Critical Value:

- Based on the significance level, find the critical value that divides the probability distribution into two regions: rejection and non-rejection.

5. Conducting the Test:

- Compare the test statistic to the critical value. If the test statistic is outside the critical region, reject H0. Otherwise, fail to reject H0.

6. Making a Conclusion:

- If H0 is rejected, conclude that there is significant evidence to support Ha.
- If H0 is not rejected, conclude that there is insufficient evidence to support Ha.

Types of Hypothesis Tests:

- One-sample tests: Compare a sample mean or proportion to a hypothesized population value.
- Two-sample tests: Compare means or proportions between two samples.
- Correlation tests: Test the relationship between two variables.

Assumptions of Hypothesis Testing:

- The sample is random and representative of the population.
- The data is normally distributed or the sample size is large enough to invoke the Central Limit Theorem.
- The variances of the samples are equal (for two-sample tests).

Limitations:

- Hypothesis testing only provides evidence for or against a claim, not definitive proof.
- It is possible to make a Type I or Type II error, meaning to reject a true H0 or fail to reject a false H0.
- It is important to properly interpret the results in the context of the research question and design.
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