Question

a sample of 270 us adult workers found that 100 of them prepare their own tax returns. what is the lower bound of a 98% confidence interval for the true proportion of all us adult workers who prepare their own tax returns? round your answer to three decimal places.

Answer 1

The Lower bound will be ≈ 0.318. To find the lower bound of a 98% confidence interval for the true proportion of all US adult workers who prepare their own tax returns, use the formula Lower bound = Point estimate - Margin of error.

Step-by-step explanation:

To find the lower bound of a 98% confidence interval for the true proportion of all US adult workers who prepare their own tax returns, we can use the formula:

Lower bound = Point estimate - Margin of error

The point estimate is the proportion of the sample that prepared their own tax returns, which is 100/270. The margin of error can be calculated as:

Margin of error = Z * sqrt((p * (1-p)) / n)

Where Z is the Z-score for a 98% confidence level (2.33), p is the proportion from the sample (100/270), and n is the sample size (270).

Plugging in the values:

Lower bound = (100/270) - (2.33 * sqrt((100/270) * (1-(100/270)) / 270))

Rounding the answer to three decimal places:

Lower bound ≈ 0.318