Question

1 Errors & Significance

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, the project will be ended.

1. State the null and alternative hypotheses that the researchers should test. Use u_d to denote the mean weight loss computed as beginning weight minus final weight.
2. 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 0.475 pound with a standard deviation of 3.978 pounds. Their p-value is 0.0039

1. Using the alpha level you selected in part e, are their results statistically significant? Explain why or why not.
2. Are their results practically significant? Explain why or why not.

Answer 1

Ans:

a)

Let   be the mean weight loss computed as beginning weight minus final weight.

b)alpha=0.05 (use alpha which is neither too small nor too large)

a)p-value=0.0039

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is significant weight loss by using new supplement.

b)Results may not be practically significant,as sample taken in above case is very large,so p-value is small and results are significant,But if small is taken,test statistic will be small and p-value will be large and result may be not have significance.