Question

You wish to test the following claim ( H a H a ) at a significance level of α = 0.02 α = 0.02 . H o : p = 0.77 H o : p = 0.77 H a : p < 0.77 H a : p < 0.77 You obtain a sample of size n = 558 n = 558 in which there are 423 successful observations. Assume the normal distribution applies.

What is the critical value for this test?

critical value =

What is the test statistic for this sample?

test statistic =

Answer 1

Solution :

Given that,

This a left (One) tailed test.

Critical value of  the significance level is α = 0.02, and the critical value for a two-tailed test is

= -2.054

= x / n = 423 / 558 = 0.76

Test statistics

z = ( - ) / *(1-) / n

= ( 0.76 - 0.77) / (0.77*0.23) / 558

= -0.561