Asked by Kamal Kaley on Apr 27, 2024
Verified
A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years.The 95% confidence interval for the true average age of all students in the university is
A) 24.6 to 25.4.
B) 24.5 to 25.5.
C) 23.0 to 27.0.
D) 20.0 to 30.0.
Confidence interval
A gamut of numbers, produced from sample statistics, believed to enfold the covert value of a population parameter.
Sample standard deviation
A statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
True average age
The actual mean age of all individuals in a specified group or population.
- Achieve competency in computing and understanding confidence intervals for population means and proportions.
Verified Answer
WZ
Willian ZhangMay 04, 2024
Final Answer :
B
Explanation :
For a 95% confidence interval, we use a z-score of 1.96. The formula for the confidence interval is:
sample mean ± (z-score) x (standard deviation/sqrt(sample size))
Plugging in the given values, we get:
25 ± (1.96) x (2/sqrt(64))
= 25 ± 0.5
So, the 95% confidence interval is from 24.5 to 25.5. Therefore, the correct answer is choice B.
sample mean ± (z-score) x (standard deviation/sqrt(sample size))
Plugging in the given values, we get:
25 ± (1.96) x (2/sqrt(64))
= 25 ± 0.5
So, the 95% confidence interval is from 24.5 to 25.5. Therefore, the correct answer is choice B.
Learning Objectives
- Achieve competency in computing and understanding confidence intervals for population means and proportions.