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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?

A

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

B

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

C

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

D

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

E

The claim is invalid since many separate significance tests were performed

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