Question

Yun wants to build a one-sample z-interval with 82% confidence to estimate what proportion of users will click an advertisement that appears on his website. He takes a random sample of 2000 users and finds that 34 of them clicked the advertisement. Approximately, what critical value z* should Yun use to construct this confidence interval?

a. z+=0.85
b. z+=1.35
c. z+=1.30
d. z+=0.92

Answer 1

To construct a one-sample z-interval with 82% confidence, the critical value z* should be approximately 1.35. Option B is the correct answer.

Step-by-step explanation:

To construct a one-sample z-interval with 82% confidence, we need to find the critical value z*.

Since we want an 82% confidence interval, the area in the tail is (1-0.82) = 0.18.

To find the critical value z* that corresponds to an area of 0.18 in the tail, we can use a standard normal distribution table or a calculator. The nearest value to 0.18 in the table is 0.1736, which corresponds to a critical value z* of approximately 1.35, so the correct answer is (b) z+ = 1.35.

To establish a one-sample z-interval with an 82% confidence level, determining the critical value, denoted as z*, is crucial. With the tail area being 0.18 for an 82% confidence interval, consulting a standard normal distribution table yields the closest value, 0.1736, corresponding to a z* of approximately 1.35.

Therefore, the correct answer is (b) z+ = 1.35, aligning with the desired confidence level and providing a precise basis for constructing the interval.