Final answer:
Alpha is the probability of a Type I error, and it is set before conducting a hypothesis test. Common alpha values are 0.10, 0.05, and 0.01. When a p-value is less than alpha, the null hypothesis is rejected.
Step-by-step explanation:
The statements concerning alpha pertain to the concept of hypothesis testing in statistics. Alpha represents the probability of committing a Type I error, which is the error of rejecting a true null hypothesis. Common values for alpha are 0.10, 0.05, and 0.01, but not 1.00 as it would indicate certainty of committing a Type I error, which is not plausible in hypothesis testing. Concerning the given statements, (c) 'Alpha is the probability of a Type 1 error' is true, and (d) 'When the p-value is smaller than the alpha, we reject the null hypothesis' is also true. A high alpha does not prove that the alternative hypothesis is true, and thus statement (a) is incorrect. Additionally, statement (b) is incorrect because while 0.10 and 0.05 are possible values of alpha, 1.00 is not a valid value for alpha as it would imply a 100% chance of rejecting a true null hypothesis. In practical terms, if the p-value obtained from a statistical test is less than the chosen alpha level, there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis as illustrated in several provided examples.