1. Understanding levels of signi?cance. Explain in plain language why a signi?cance test that is signi?cant at the 1% level must always be signi?cant at the 5% level.

2. More  on  understanding  levels  of  signi?cance.  You are told that a signi?cance test is  signi?cant  at the 5% level. From this information can you determine whether or not it is signi?cant at the 1% level? Explain your answer.

3. Test statistic  and  levels  of  signi?cance. Consider a signi?cance test for a null hypothesis versus a two-sided alternative with a z test statistic. Give a value of z that will give a result signi?cant at the 0.5% level but not at the 0.1% level.

4. Using Table D to ?nd a P-value. You have performed a two-sided test of signi?cance and obtained a value of z = 3.1. Use Table D to ?nd the approximate P-value for this test.

5. More on using Table D to ?nd a P-value. You have performed a one-sided test of signi?cance and obtained a value of z = 0.35. Use Table D to ?nd the approximate P-value for this test.

7. Using Table A and Table D to ?nd a P-value. Consider a signi?cance test for a null hypothesis versus a two-sided alternative. Between what values from Table D does the P-value for an outcome z = 1.37 lie? Calculate the P-value using Table A, and verify that it lies between the values you found from Table D.

8. More on using Table A and Table D to ?nd a P-value. Refer to the previous exercise. Find the P-value for z = -1.37.