When is it appropriate to use the t test?

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In summary, the t test is used to analyze the difference between two means of a continuous variable in a sample. It is appropriate for continuous data that follows a normal distribution, and can be used for both one-tailed and two-tailed tests depending on the researcher's hypothesis. Non-parametric data cannot be analyzed using a t test, and the results of a t test can be interpreted based on the p-value, with a p-value less than 0.05 indicating a significant difference between the two groups being compared.
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Homework Statement



If i have data and want to compare the two means, when is it appropriate to use the t test?

The Attempt at a Solution



i know its because the distribution is normal but there are also other reasons.
Thank you.
 
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the t-test is used when the sample size is "small" less than 30 and the underlying distribution is normal.
 

1. When is the t test used?

The t test is used when analyzing the difference between two means of a continuous variable in a sample. It is commonly used in research studies and experiments to determine if there is a significant difference between two groups.

2. What type of data is appropriate for a t test?

A t test is appropriate for analyzing continuous data, which is numerical data that can take on any value within a range. It is important that the data follows a normal distribution, which means that the data is evenly spread out around the mean.

3. When should a one-tailed vs. two-tailed t test be used?

A one-tailed t test is used when the researcher has a specific hypothesis about the direction of the difference between the two groups. A two-tailed t test is used when there is no specific hypothesis about the direction of the difference, and the researcher wants to test for any difference between the two groups.

4. Can a t test be used for non-parametric data?

No, a t test is only appropriate for parametric data. Non-parametric data does not follow a normal distribution and therefore cannot be analyzed using a t test. In this case, non-parametric tests such as the Wilcoxon rank-sum test or Mann-Whitney U test should be used instead.

5. How do I interpret the results of a t test?

The results of a t test will provide a p-value, which indicates the probability of obtaining the observed difference between the two groups if there is no true difference in the population. A p-value less than 0.05 is typically considered statistically significant, meaning that there is a low probability of obtaining this result by chance. This would suggest that there is a significant difference between the two groups being compared.

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