Question

a. For the following degrees of freedom, list the critical values for a one-tailed and two-tailed test at a .01 and .05 level of significance.

.01 .05

df =  (Infinity) ___ ___ (One-tailed test)

df =  (Infinity) ___ ___ (Two-tailed test)

b. Refer to Table 8.4 in Chapter 8. How do the critical values you listed in the previous question compare with those listed for the z-distribution. Explain.

Answer 1

Solution

a) The critical values for One-tailed and Two-tailed test at 0.01 & 0.05 level of significance for degrees of freedom at infinity is given below

One tailed test

At 0.01 level of significance df = infinity the critical value is 2.326

At 0.05 level of significance df = infinity the critical value is 1.645

Two tailed test

At 0.01 level of significance df = infinity the critical value is 2.576

At 0.05 level of significance df = infinity the critical value is 1.960

b) For the z- distribution

taking the above critical values as z value

1.645=0.9495 = lower limit of right 5% tail

1.96=0.9750 = lower limit of right 2.5% tail

2.32=0.9898 = lower limit of right 1% tail

2.57=0.9949 = lower limit of right 0.5% tail