Asked by Sydnee Smith on May 10, 2024
Verified
A random sample of 25,000 ACT test takers had an average score of 21 with a standard deviation of 5.With a .95 probability, determine the margin of error.
A) .0277
B) .0568
C) .2603
D) .0620
Margin of Error
Indicates the confidence in the precision of a survey or poll result, quantifying potential deviation from the true population value.
Standard Deviation
An indicator of the range or distribution of a data set, showing the degree to which the values diverge from the average.
ACT Test Takers
Individuals who participate in taking the ACT, a standardized test used for college admissions in the United States.
- Appreciate the influence of sample size and confidence levels on the accuracy of the margin of error and the formulation of confidence intervals for population means and proportions.
Verified Answer
RL
Ricardo LanderosMay 15, 2024
Final Answer :
D
Explanation :
The formula for the margin of error is:
Margin of error = z * (standard deviation / sqrt(sample size))
We need to find the z-value corresponding to a .95 probability. This is the same as finding the z-value that leaves .025 in the upper tail of the standard normal distribution. Using a z-table, we find that z = 1.96.
Plugging in the values,
Margin of error = 1.96 * (5 / sqrt(25000))
Margin of error = 0.062
Therefore, the margin of error is 0.062 or approximately 0.06. So the correct answer is D.
Margin of error = z * (standard deviation / sqrt(sample size))
We need to find the z-value corresponding to a .95 probability. This is the same as finding the z-value that leaves .025 in the upper tail of the standard normal distribution. Using a z-table, we find that z = 1.96.
Plugging in the values,
Margin of error = 1.96 * (5 / sqrt(25000))
Margin of error = 0.062
Therefore, the margin of error is 0.062 or approximately 0.06. So the correct answer is D.
Learning Objectives
- Appreciate the influence of sample size and confidence levels on the accuracy of the margin of error and the formulation of confidence intervals for population means and proportions.