Question

in hypothesis testing, if the significance level is set to 0.01, this indicates:
a. a 1% chance that the null hypothesis is true.
b. that the p - value must be greater than 0.01 to reject the null hypothesis.
c. a 99% probability that the results are not due to chance.
d. a 1% risk of committing a type i error, rejecting the null hypothesis when it is true.

Explanation:

• Option a: The significance level is not about the chance of the null hypothesis being true.
• Option b: We reject the null hypothesis when the p - value is less than the significance level (0.01 in this case), not greater.
• Option c: While a lower significance level gives more confidence, it's not directly stated as a 99% probability that results are not due to chance in this context.
• Option d: The significance level ($\alpha$) is the probability of Type I error (rejecting the null hypothesis when it is true). When $\alpha = 0.01$, there is a 1% risk of Type I error.

Answer:

d. A 1% risk of committing a Type I error, rejecting the null hypothesis when it is true.