Question

According to a poll, 40% of Americans read, print books exclusively, rather than reading some digital books suppose a random sample of 300 Americans is selected to complete parts a through D below. What is the standard error for the sample proportion?

Answer 1

The standard error for the sample proportion of Americans who read print books exclusively, based on a sample of 300, is approximately 0.0283 or 2.83%.

Step-by-step explanation:

To calculate the standard error for the sample proportion, we need to use the formula for standard error (SE) of a proportion, which is SE = √[p(1-p)/n], where p is the sample proportion and n is the sample size. Given that 40% of Americans read print books exclusively, we set p = 0.40. The sample size, n, is 300. Plugging the values into the formula, we get SE = √[0.40(1-0.40)/300].

To proceed with the calculation:

1. First, calculate the product of p and 1-p: 0.40 × 0.60 = 0.24.
2. Next, divide this product by the sample size: 0.24 / 300 = 0.0008.
3. Finally, take the square root of the result: √0.0008 ≈ 0.0283.

The standard error for the sample proportion is approximately 0.0283 or 2.83%.