Final Answer:
The statement is false. When dealing with statistical tests, a probability level of 0.05 or below does not automatically lead to the acceptance of the alternative hypothesis; rather, it allows the rejection of the null hypothesis (Option b).
Step-by-step explanation:
In statistical hypothesis testing, the significance level (often denoted as α) is set to determine the threshold for accepting or rejecting the null hypothesis. The conventional threshold is 0.05, meaning that if the probability of obtaining the observed results (or more extreme) under the null hypothesis is less than 0.05, the null hypothesis is rejected. It is crucial to note that the acceptance or rejection of hypotheses is based on the comparison of the p-value with the significance level, and it is the null hypothesis that is either rejected or fails to be rejected (Option b).
If the p-value is less than or equal to the significance level, typically 0.05, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected. Therefore, the statement that the alternative hypothesis is automatically accepted when the results are at a probability of 0.05 or below is inaccurate. The decision to accept or reject the alternative hypothesis depends on a careful evaluation of the p-value in relation to the chosen significance level.
In summary, statistical hypothesis testing involves a nuanced interpretation of p-values and significance levels. A p-value of 0.05 or below does not warrant automatic acceptance of the alternative hypothesis but rather serves as a criterion for rejecting the null hypothesis based on a predetermined level of significance.