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Shawna has incorporated a new workout plan. She wants to lower the Body Mass Index (BMI) of her clients. Her clients’ average BMI is 28. After implementing the workout plan, the average BMI of her clients is 21. Shawna used software to simulate 25 trials of the mean differences in BMI. Find Shawna’s mean difference and determine whether the change is significant and if it’s a plausible result. (1 point) Responses The difference between the means is 7, so it is not a plausible result. The difference between the means is 7, so it is not a plausible result. The difference between the means is 7, so it is a plausible result. The difference between the means is 7, so it is a plausible result. The difference between the means is 4, so it is a plausible result. The difference between the means is 4, so it is a plausible result. The difference between the means is 3, so it is not a plausible result.

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To find Shawna's mean difference in BMI, we can subtract the average BMI after implementing the workout plan from the average BMI before the plan.

  1. Average BMI before the workout plan = 28
  2. Average BMI after the workout plan = 21

Mean difference = Average BMI before - Average BMI after Mean difference = 28 - 21 = 7

The mean difference is 7.

To determine if this change is significant and plausible, we would typically consider the context of the data and the results from the simulations. If the software Shawna used suggests that this mean difference is outside of the expected range based on the trials, then it could be deemed not plausible. However, if the simulated results show that a mean difference of 7 is within a reasonable range of fluctuations (taking into account normal variability in BMI changes), then it could be plausible.

Given the options provided:

  1. The difference between the means is 7, so it is not a plausible result.
  2. The difference between the means is 7, so it is not a plausible result.
  3. The difference between the means is 7, so it is a plausible result.
  4. The difference between the means is 7, so it is a plausible result.
  5. The difference between the means is 4, so it is a plausible result.
  6. The difference between the means is 4, so it is a plausible result.
  7. The difference between the means is 3, so it is not a plausible result.

Since we have determined that the difference between the means is 7, we must decide on whether it is plausible based on the simulated results. Without additional context about the simulations, it is unclear, but in statistical analysis, a large difference can be significant.

If we assume that a mean difference of 7 could reasonably occur based on Shawna's evidence or prior knowledge, the plausible responses regarding the difference would be options 3 or 4.

Based on typical reasoning, if the simulations for mean differences showed results that could accommodate a difference of 7, we would conclude:

The difference between the means is 7, so it is a plausible result.