Question

In a poll, 74% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder?" The margin of error in the poll was 4%, and the estimate was made with 90% confidence.

How many people were surveyed?

How do you step by step solve this with a TI-84 Calculator? What function can you use?

Answer 1

324

Explanation:

given that in a poll, 74% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder?"

i.e. Sample proportion
`p=0.74\\q =1-p =0.26\\`

Margin of error = 4% = 0.04

Confidence level =90%

Z critical value for 90% = 1.645

Margin of error = 1.645 * std error

Hence std error =
`(0.04)/(1.645) \\=0.0243`

Std error is also equal to

`\sqrt{(pq)/(n) } =\sqrt{(0.74(0.26))/(n) } =0.0243\\√(n) =18..05\\n = 325.83~324`

Sample size should be 324.

The formula is sample size = (Z critical value)^2 (pq)/(Margin of error )^2