Final Answer:
The probability of rejecting a null hypothesis that is actually true when B=0.34 and a=0.01 is C. 0.66.
Step-by-step explanation:
In hypothesis testing, the probability of making a Type I error (rejecting a null hypothesis when it's true) is denoted by the symbol alpha (α). In this scenario, alpha is given as a=0.01. This represents the significance level, the threshold beyond which we would reject a true null hypothesis. Therefore, the probability of making a Type I error is equal to the significance level, which is 0.01.
The probability of rejecting a true null hypothesis is calculated as 1 - α. In this case, 1 - 0.01 = 0.99. This implies that there is a 99% chance of correctly accepting the null hypothesis when it's true. The provided options (A. 0.01, B. 0.34, C. 0.66, D. 0.99) correspond to these probabilities, and the correct answer is C. 0.66, which is the probability of rejecting a null hypothesis that is actually true.
It's crucial to understand the significance level and the balance between Type I and Type II errors in hypothesis testing. The chosen significance level, in this case, a=0.01, influences the trade-off between the risk of incorrectly rejecting a true null hypothesis and failing to reject a false null hypothesis. A lower significance level reduces the risk of Type I errors but increases the risk of Type II errors.