169k views
4 votes
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.

1 Answer

2 votes

Final answer:

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.

User Gpullen
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.