Asked by The Gibson Family on May 03, 2024
Verified
Calculate the 99% confidence interval for a sample of N = 30 with a mean 
= 1376.41 and standard error of the mean 
= 30.73.
A) 99% CI = 1376.41 ± 62.84
B) 99% CI = 1376.41 ± 52.15
C) 99% CI = 1376.41 ± 84.81
D) 99% CI = 1376.41 ± 33.48
Confidence Interval
A swath of values, taken from statistical analyses of a sample, anticipated to hold within it the value of a not-yet-known population trait.
Standard Error
The standard deviation of the sampling distribution of a statistic, typically the mean.
Mean
The average value of a set of numbers, calculated by dividing the sum of all values by the number of values.
- Determine specific confidence intervals based on sample statistics.
Verified Answer
CI = X̄ ± t(α/2, n-1) * SEM
where X̄ is the sample mean, SEM is the standard error of the mean, n is the sample size, and t(α/2, n-1) is the t-score for the desired level of confidence and degrees of freedom.
For a 99% confidence interval with 30 degrees of freedom, we use t(α/2, n-1) = 2.750.
Substituting the given values into the formula, we get:
CI = 1376.41 ± 2.750 * 30.73
CI = 1376.41 ± 84.81
Therefore, the correct choice is C.
Learning Objectives
- Determine specific confidence intervals based on sample statistics.
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