Answer:
Explanation:
Hello!
There are two possibilities regarding a hypothesis, this can either be true or false and there are also two possible decisions when conducting a hypothesis test you either reject the null hypothesis or do not reject it. These make four possible scenarios:
1. Reject the null hypothesis when the hypothesis is false (This is a correct decision) With probability 1-β (Known as the power of the test)
2. Reject the null hypothesis when the hypothesis is true (This decision is also known as Type I error) With probability α (Known as significance level)
3. Fail to reject the null hypothesis when the hypothesis is true (This is a correct decision) With probability 1-α.
4. Fail to reject the null hypothesis when the hypothesis is false (This decision is also known as Type II error) With probability β.
In this example the claim is "At least 2/3 of dieters regain the weight they lost from dieting" we can rewrite it as the proportion of dieters that regain their lost weight is at least 0.67, symbolically:
H₀: p ≥ 0.67
After conducting the hypothesis test, the decision was to not reject the null hypothesis.
If it is known that the actual percentage of dieters that regain their lost weight is 0.6, symbolically p=0.6, then the null hypothesis is false.
The situation you are in is that you failed to reject a false null hypothesis, this is a Type II error.
I hope it helps!