Question

a significance level for a hypothesis test is given as alpha=0.1. Interpret this value - The smallest value of alpha that you can use and still reject Null hypothesis is 0.01. - The probability of making a Type II error is 0.99. - There is a 1% chance that the sample will be biased. - The probability of making a Type I error is 0.01. With explanation, please.

Answer 1

The significance level of 0.1 implies there's a 10% chance of incorrectly rejecting a true null hypothesis (Type I error), not a 1% chance as the question's statement incorrectly suggests.

Step-by-step explanation:

The significance level of a hypothesis test, denoted as alpha (α), represents the probability of making a Type I error, which occurs if we reject the null hypothesis when it is actually true. When the significance level is set to 0.1 or 10%, it means that there's a 10% chance of rejecting a true null hypothesis, not a 1% chance as the question proposes. The smallest value of α that you can use and still reject the null hypothesis being 0.01 would indicate a stricter test with a 1% risk of a Type I error, but this is a separate scenario and not the case for an α of 0.1. The probability of making a Type II error, which is not rejecting a false null hypothesis, is not specified by the alpha value and must be calculated separately considering the power of the test.

Answer 2

The level of significance (α = 0.1) represents a 10% chance of making a Type I error, which is rejecting the null hypothesis when it is actually true, not 0.01 as the question incorrectly states.

Step-by-step explanation:

The level of significance of the test, denoted as α, is the probability of making a Type I error if the null hypothesis is actually true. In this case, with α = 0.1 (10%), the level of significance implies that if the null hypothesis is true, there is a 10% chance of incorrectly rejecting it. This probability of a Type I error corresponds to the available evidence considered strong enough to reject the null hypothesis in this context.

From the given options, the correct interpretation is: 'The probability of making a Type I error is 0.01'. However, this statement is inaccurate given the α value of 0.1. The correct statement should be 'The probability of making a Type I error is 0.1'.