Final answer:
To estimate the proportion of adults that would like to travel to outer space, we can construct a 95% confidence interval. Given a sample of 329 out of 763 adults who would like to travel to outer space, the 95% confidence interval is approximately 0.396 to 0.466.
Step-by-step explanation:
To estimate the proportion of adults that would like to travel to outer space, we can construct a 95% confidence interval. Given that 329 out of 763 adults surveyed would like to travel to outer space, the sample proportion is 329/763 = 0.431. We can use the formula for a confidence interval for a proportion:
Confidence Interval = sample proportion ± margin of error
The margin of error can be calculated as:
Margin of Error = critical value * standard error
Since we want a 95% confidence interval, the critical value is 1.96 (z-score for a confidence level of 95%). The standard error can be calculated as:
Standard Error = sqrt((sample proportion * (1 - sample proportion)) / sample size)
Using these formulas, we can plug in the values and calculate the confidence interval:
Sample Proportion = 0.431
Sample Size = 763
Standard Error = sqrt((0.431 * (1 - 0.431)) / 763)
≈ 0.018
Margin of Error = 1.96 * 0.018
≈ 0.035
Confidence Interval ≈ 0.431 ± 0.035
Therefore, the 95% confidence interval for the proportion of adults that would like to travel to outer space is approximately 0.396 to 0.466.