Question

A college research group reported that 46​%

of college students aged​ 18-24 would spend their spring breaks relaxing at home in 2009. A sample of 155
college students was selected. Complete parts a through d below.
a. Calculate the standard error of the proportion.

Answer 1

To calculate the standard error of the proportion for a given sample, use the formula SE = sqrt((p * (1 - p)) / n), where p is the proportion and n is the sample size. In this case, the proportion is 0.46 and the sample size is 155, resulting in a standard error of approximately 0.0401.

Step-by-step explanation:

To calculate the standard error of the proportion, we can use the formula:

SE = sqrt((p * (1 - p)) / n)

Where:

• SE is the standard error of the proportion
• p is the proportion (in decimal form)
• n is the sample size

In this case, the proportion is 0.46 (46%) and the sample size is 155. So, the calculation would be:

SE = sqrt((0.46 * (1 - 0.46)) / 155)

Plugging in the values, we get:

SE ≈ sqrt(0.2492 / 155) ≈ sqrt(0.001607) ≈ 0.0401

Therefore, the standard error of the proportion is approximately 0.0401.