To determine a 72 percent level of confidence for a proportion, the value of z is approximately.

Solution:

The determination of a 72 percent level of confidence for a proportion can be visualized under two scenarios.

Scenario 1: Two Tail Test

In this case the z-value corresponding to the confidence level of 72% exists on both sides of the centre of the normal distribution which means that 36% lies on both sides of the centre line.

Therefore level of significance (ɑ) =(0.5 - 0.36) = 0.14). The diagram below describes scenario 1. The z value from the normal distribution table is1.08 The two tailed test is used when actual proportion of a sample can be on the either side of population proportion.

Scenario 2:

In the case of one tail test the area of 0.72 is considered from left most point of the normal distribution as shown below. However the value of z remains the same i.e. z = 0.58. The shaded area shown below is considered from the left hand side.

z = 0.58

To determine a 72 percent level of confidence for a proportion, the value of z is approximately.

Summary:

72 percent level of confidence for a proportion means that the value of z is approximately.1.08 or 0.58 as depending on the type of test used (one tail or two tail test)