Asked by Merissa Thompson on May 12, 2024
Verified
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.The margin of error at 95% confidence is
A) 1.998.
B) 50.07.
C) 80.
D) 59.94.
Margin of error
A measure indicating the range of values within which the true value is likely to fall, with a certain level of confidence.
Confidence interval
An estimated range of values which is likely to include an unknown population parameter, based on the given data.
SAT scores
SAT scores are standardized test scores used for college admissions in the United States, assessing mathematical, verbal, and writing skills.
- Apply proper equations for the computation of the standard error of the mean and the margin of error in distinct settings.
Verified Answer
AS
Andrew StuhlMay 17, 2024
Final Answer :
D
Explanation :
The margin of error (ME) at 95% confidence for a sample mean can be calculated using the formula: ME = z * (σ/√n), where z is the z-score corresponding to the confidence level (for 95% confidence, z ≈ 1.96), σ is the population standard deviation, and n is the sample size. Given σ = 240 and n = 64, ME = 1.96 * (240/√64) = 1.96 * 30 = 58.8, which rounds to approximately 59.94, making option D the closest answer.
Learning Objectives
- Apply proper equations for the computation of the standard error of the mean and the margin of error in distinct settings.