Question

1. A team of researchers has developed a new weight loss supplement. They want to know if patients who use

the new supplement for four weeks lose any weight. The supplement has some minor side effects including mild headaches and achiness. If the researchers obtain evidence of weight loss they will proceed to produce the supplement commercially and sell it for a large profit. If they do not obtain evidence of weight loss they will end the project. [21 points—3 pts each]

A. State the null and alternative hypotheses that the researchers should test. Use md to denote the mean weight loss computed as beginning weight minus final weight. 

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?

D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious?  Explain your reasoning.

E. If you were working with this research team, what alpha level would you use? Explain your reasoning.

Assume that the research team completes this study with a sample size of 500 and finds a mean weight loss of 0.475pound with a standard deviation of 3.978 pounds. Their p-value is 0.0039

F. Using the alpha level you selected in part E, are their results statistically significant? Explain why or why not.

G. Are their results practically significant? Explain why or why not.

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