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Appropriate statistic tests

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I have created the following hypothesis need help for approprate tests ( independant t test /correlation/regression/anova) and stating the hypothesis

1. What would you suggest to be the appropriate statistic tests to use and why ?

2. Any suggestions on stating the hypothesis in a more professional manner?
This is what I have so far

Null Hypothesis #1. There is no relationship between episodes of bullying and post-traumatic stress disorder.

Alternative Hypothesis #1. Post-traumatic stress disorder is directly related to episodes of bullying.

Null Hypothesis #2. There is no relationship with the severity of bullying episodes and post-traumatic stress disorder.

Alternative Hypothesis #2. The severity of bullying episodes is related to post-tramatic stress disorder.

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Solution Summary

This solution is comprised of a detailed explanation on appropriate statistic method used for the objectives defined in the problem. Full description is given for the method along with the null and alternative hypotheses is provided in the solution.

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Null Hypothesis #1: There is no linear relationship between episodes of bullying and post-traumatic stress disorder. Or The episodes of bullying and post-traumatic stress disorder are independent of each other.

Alternative Hypothesis #1: There is a linear relationship between episodes of bullying and ...

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