Question

A bank randomly selected 252 checking account customers and found that 113 of them also had savings accounts at this same bank. Construct a 90% confidence interval for the true proportion of checking account customers who also have savings accounts. (Give your answers correct to three decimal places.)

Lower Limit -

Upper Limit -

Answer 1

The general formula for a confidence interval, the confidence interval for a true proportion, is:

p ± z σ_p

where p is the proportion in the sample, z depends on the level of confidence desired, and σ_p is the standard error of a proportion, given by

where  n is the sample size.

In this context:

Sample proportion

(level of significance)

( from the table )

90% confidence interval for the true proportion is :

p ± z_0.1 σ_p

0.448± 1.64*0.0308

0.448± 0.0505

Lower Limit - 0.448- 0.0505 = 0.3975 = 0.400 (three decimal places)

Upper Limit - 0.448+ 0.0505 = 0.4985 = 0.500 (three decimal places)