1. Explain why the following statements are true or false. (a) A significance te

Question

1. Explain why the following statements are true or false.

(a) A significance test that is significant at the 5% level must always be significant at the 10% level.

(b) A null hypothesis rejected at the 5% significance level must also be rejected at the 10% significance level.

(c) Failing to reject the null hypothesis at the 5% significance level must also mean failing to reject the null hypothesis at the 10% significance level.

(d) A test statistic that is significant at the 0.05 level implies that there is a 5% probability that the null hypothesis is true.

Explanation / Answer

a) Yes, it is true. A significance test that is significant at the 5% level must always be significant at the 10% level because if the test is significant level, then it will also significant at all levels greater than 10%

b) Yes, it is true. A null hypothesis rejected at the 5% significance level must also be rejected at the 10% significance level. It has same explaination as above because it is same as part a)

c) No, it is not true because if p value is 0.06,it is not significant at 5% but significant at 10%

d) Yes, it is true, It means probability of reject the null hypothesis when it is true

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