Question

Write a conclusion for the researcher. (Assume α is 0.1 or less.)

A. Because this probability is small, reject the null hypothesis. There is sufficient evidence to conclude that the dart-picking strategy resulted in a majority of winners.
B. Because this probability is small, do not reject the null hypothesis. There is not sufficient evidence to conclude that the dart-picking strategy resulted in a majority of winners.
C. Because this probability is not small, do not reject the null hypothesis. There is not sufficient evidence to conclude that the dart-picking strategy resulted in a majority of winners.
D. Because this probability is not small, reject the null hypothesis. There is sufficient evidence to conclude that the dart-picking strategy resulted in a majority of winners

Answer 1

If the p-value is smaller than the significance level (α), the null hypothesis is rejected, indicating sufficient evidence against it.

Step-by-step explanation:

When considering whether to reject the null hypothesis in hypothesis testing, we're guided by the probability value, or p-value, in comparison to our chosen significance level (α). You make a decision based on whether the p-value is less than or greater than α. In cases where α > p-value, you would reject the null hypothesis, suggesting that the outcome is statistically significant and that there is sufficient evidence against the null hypothesis. Conversely, if α ≤ p-value, you do not reject the null hypothesis, indicating that there's insufficient evidence to support an effect.

In your query, assuming α is 0.1 or less, if a researcher finds the p-value to be small, they should reject the null hypothesis. Therefore, the appropriate conclusion would be:

Because this probability is small, reject the null hypothesis. There is sufficient evidence to conclude that the dart-picking strategy resulted in a majority of winners.