Question

If a hypothesis is rejected at the 10% level of significance (i.e. 90% confidence), it

Group of answer choices

1. will not be rejected at 5% significance.

2. will always be rejected at 5% significance.

3. may or may not rejected at 5% significance.

Answer 1

Correct option is:

3. may or may not rejected at 5% significance.

(since rejection at 10% level tells us that p value is less than 10% but does not give clarity if it is less than 5% or more than 5% , therefore we can not decide at 5% level)

Answer 2

The correct answer is:

3. may or may not be rejected at 5% significance.

Explanation:

• 10% significance level (α = 0.10): If the p-value of the test is less than 0.10, the hypothesis is rejected at this level.

• 5% significance level (α = 0.05): This is a stricter threshold. If the p-value is:

• Less than 0.05: The hypothesis will also be rejected at 5% (since it's already rejected at 10%).

• Between 0.05 and 0.10: The hypothesis is rejected at 10% but not at 5%.

  
  

Thus, rejection at 10% does not guarantee rejection at 5%. The outcome depends on the p-value