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A dietician tests a new diet plan on $20\text{ groups of people}$, with $14\text{ people in each group}$. All participants were randomly selected from a large group of volunteers, and all participants followed the diet plan.

Two months later, the dietician obtains the sample mean weight loss and standard deviation for each group and performs $20$ one-sample $t$-tests. She notes that one of these tests is statistically significant, with a $p$-value of $0.034$.

She then touts her diet plan on a television infomercial, claiming that her plan results in significant weight loss at an $\alpha = 0.05$ significance level.

What can be said about her claim?


The claim is valid because she used appropriate sampling techniques and appropriate statistical methods for each group.


The claim is valid because she was able to reject the null hypothesis at an acceptable level of significance.


The claim is valid because subjects in one group lost a significant amount of weight.


The claim is invalid because people did not lose weight on her diet plan.


The claim is invalid since many separate significance tests were performed

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