Question

a recent survey of 349 people ages 18 to 29 found that 86% of them own a smartphone. find the 99% confidence interval of the population proportion

Answer 1

To compute the 99% confidence interval for the population proportion, we can use the formula: lower bound = sample proportion - margin of error, upper bound = sample proportion + margin of error. Plugging in the given values, we get a confidence interval of (0.8199, 0.9001).

Step-by-step explanation:

To compute the 99% confidence interval for the population proportion, we can use the formula:

lower bound = sample proportion - margin of error

upper bound = sample proportion + margin of error

To calculate the margin of error, we need to use the formula:

margin of error = Z * sqrt((sample proportion * (1 - sample proportion)) / sample size)

Substituting the given values, we have:

sample proportion = 0.86

sample size = 349

Z = 2.58 (from the standard normal distribution table for a 99% confidence level)

Plugging in these values, we get:

margin of error = 2.58 * sqrt((0.86 * (1 - 0.86)) / 349) ≈ 0.0401

Therefore, the 99% confidence interval for the population proportion is approximately 0.86 ± 0.0401, or (0.8199, 0.9001).