Question

In a survey of 1,713 US adults, 1,352 said they had paid a bill online within the past year. What is the LOWER endpoint of a 90% confidence interval for the population proportion?

Answer 1

To find the lower endpoint of a 90% confidence interval for the population proportion, one must calculate the sample proportion, standard error, and use the Z-score for 90% confidence level to subtract the margin of error from the sample proportion. The calculation shows that at least 77.3% of American adults have paid a bill online within the past year.

Step-by-step explanation:

To calculate the lower endpoint of a 90% confidence interval for the population proportion, we can use the following formula:

Lower endpoint = π' - Z * √(π'(1 - π') / n)

where:

• π' is the sample proportion (1352/1713)
• Z is the Z-score corresponding to the desired confidence level (for 90%, Z is approximately 1.645)
• n is the sample size (1713)

First, we find the sample proportion:

π' = 1352 / 1713 ≈ 0.789

Then, calculate the standard error of the proportion:

SE = √(π'(1 - π') / n) ≈ √(0.789(1 - 0.789) / 1713) ≈ 0.010

Finally, calculate the lower endpoint of the confidence interval:

Lower endpoint = π' - Z * SE ≈ 0.789 - 1.645 * 0.010 ≈ 0.773

We can be 90% confident that the true population proportion of American adults who have paid a bill online within the past year is at least 0.773, or 77.3%.