Question

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. Type I Error:
   1. What does a Type I error mean in this situation? Be sure your answer specifically states the error in terms of this scenario.
3. 2. What are the consequences of making a Type I error in this scenario?
4. Type II Error:
   1. What does a Type II error mean in this situation? Be sure your answer specifically states the error in terms of this scenario.
5. 2. What are the consequences of making a Type II error in this scenario?
6. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.
7. If you were working with this research team, what alpha level would you use? Explain your reasoning.

Answer 1

a.

Null Hypothesis(H0): The supplement is not effective in reducing weight. _d =​​​​​​

Alternative Hypothesis(H1): The supplement is effective in reducing weight. _d =

(W1 =average beginning weight and W2 =average final weight)

b.

i.

Type I error: Rejection of true null hypothesis(H0).

If the difference of weights is actually less than or equal to 0, i.e., the drug is not useful, we reject it and consider it is useful when in fact it is not useful in reducing weight.

ii.

Consequence: The supplement is produced but suffer losses as it does not help in reducing weight and also have side effects. So, the drug becomes dangerous. It becomes harmful instead of being useful.

d.

i.

Type II error: Failing to reject a false null hypothesis(H0).

If the difference of weights is actually not less than or equal to 0, i.e., drug is useful, we failed to reject it and consider it is not useful when in fact it is useful in reducing weight.

ii.

Consequence: The supplement will not be produced and the project will be ended. So, there will be a loss of good business opportunity due to this error.

f.

In this scenario, Type I error is more serious. It's because type I error leads to the production of harmful supplement that causes mild headaches and achiness and eventually leads to losses and so, it is harmful for both public and producers. Type II error only leads to a loss of good business opportunity, but not harmful to anyone.

g.

Alpha, is the probability(P) of making a type I error. Here, type I error is more serious and thus, the probability of making type I error should be as least as possible. Therefore, I use an alpha level of 0.01, i.e., 1%. P(type I error) = =0.01