Asked by Monica Landrum on Apr 28, 2024
Verified
Use the formula , where = to calculate the 99% confidence interval for a sample of N = 15 with a mean = 7.50 and standard deviation (s) = 1.25.
A) 99% CI = 7.50 ± .69
B) 99% CI = 7.50 ± .56
C) 99% CI = 7.50 ± .95
D) 99% CI = 7.50 ± 3.30
Confidence Interval
A span of numerical values, calculated from statistics of a sample, that is expected to encompass the value of a not yet known population parameter with a certain degree of confidence.
Sample
A subset of individuals or observations selected from a larger population for the purpose of statistical analysis.
Mean
The mean of a number set, found by dividing the total sum of the numbers by the quantity of numbers present in the set.
- Understand thoroughly the concept of confidence intervals and the approach taken to calculate them.
- Adopt the formula to gauge the 99% confidence span.
- Recognize the impact of the standard deviation and standard error on confidence intervals.
Verified Answer
CI = X̄ ± t(alpha/2, df) * (s/√n)
Where:
X̄ = sample mean
t(alpha/2, df) = t-value for the desired confidence level (alpha) and degrees of freedom (df)
s = sample standard deviation
n = sample size
Given:
X̄ = 7.50
s = 1.25
n = 15
We need to find the t-value for a 99% confidence interval and 14 degrees of freedom (df = n-1). Using a t-table or calculator, we find that t(0.995, 14) = 2.977.
Plugging in the values, we get:
CI = 7.50 ± 2.977 * (1.25/√15)
CI = 7.50 ± 0.945
Therefore, the 99% confidence interval is 7.50 ± 0.95, which is closest to option C.
Learning Objectives
- Understand thoroughly the concept of confidence intervals and the approach taken to calculate them.
- Adopt the formula to gauge the 99% confidence span.
- Recognize the impact of the standard deviation and standard error on confidence intervals.
Related questions
If a Researcher Chooses the 99% Confidence Interval Instead of ...
A Confidence Interval Using the Known Population Standard Deviation ________ ...
For a 95% Confidence Interval for a Population Mean,there Is ...
A University Is Studying the Proportion of Students Retained in ...
The Lower and Upper Limits of the 68 ...