Question

Construct a confidence interval of the population proportion at the given level of confidence.

x = 540, n = 1200, 96% confidence

Answer 1

Dear student, your question is how can we obtained the value 2.054.

This value we obtained from z score table.

We have given 96% CI and it is two sided.

96% means 0.96 and alpha = 1-0.96 = 0.04

But for two sides alpha is given as,

Alpha = 0.04/2 = 0.02

Now we don't see 0.02 in the table we see 1-alpha in the z score table.

And 1-alpha = 1-0.02 = 0.98.

Now search 0.98 in the z score table.

See the table below

See the orange square.

Now we saw the nearest value to the z score which is at 2.05 and we consider 2.05 from table

In the above problem value calculated from online calculator so it gives accurate value ie 2.054.

In this way we can saw the z score table.