Final answer:
The probability of a Type I error in a hypothesis test is fixed by the significance level set for the test. In this case, since the significance level is 5%, the probability of committing a Type I error is also 5%, regardless of the p-value.
Step-by-step explanation:
The question revolves around the concept of hypothesis testing in statistics, with specific reference to the significance level, p-value, and Type I error. The significance level, often represented as α (alpha), is the threshold below which we reject the null hypothesis.
In this case, the significance level is 5% or 0.05. A p-value is the probability of obtaining a sample result as extreme as the one observed, under the assumption that the null hypothesis is true. If the p-value is less than alpha, we reject the null hypothesis.
Regarding the possibility of a Type I error, which is the incorrect rejection of a true null hypothesis, this probability is fixed by the significance level set before testing begins. Therefore, the probability of a Type I error for this hypothesis test is the significance level itself, which is 0.05 or 5%.
In the given scenario, the p-value is 0.014, which is smaller than the significance level of 0.05. As per the conventional criteria, this would lead to a decision to reject the null hypothesis. Nonetheless, the probability of a Type I error is not equal to the p-value but is determined by the preset significance level. Hence, the correct answer to the question is 0.05, representing the fixed probability of committing a Type I error when the null hypothesis is in fact true.