Yun wants to build a one-sample z interval with 82%, percent confidence to estimate what proportion of users will click an advertisement that appears on his website. He takes a random sample of 200 users and finds that 34 of them clicked the advertisement.

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z * √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 200

x = 34

p = 34/200 = 0.17

q = 1 - 0.17 = 0.83

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.82 = 0.18

α/2 = 0.18/2 = 0.09

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.09 = 0.91

The z score corresponding to the area on the z table is 1.35. Thus, the z score for a confidence level of 82% is 1.35

Therefore, the 82% confidence interval is

0.17 ± 1.35√ (0.17) (0.83) / 200

Confidence interval is 0.17 ± 0.036