Asked by Kayla Valdes on May 02, 2024
Verified
Calculate the lower and upper limits of the 90% confidence interval for a sample of N = 29 with a mean = 137.98 and standard error of the mean = 4.98.
A) (129.51, 146.45)
B) (124.22, 151.74)
C) (131.30, 144.66)
D) (127.78, 148.18)
Confidence Interval
A range of values, derived from sample statistics, that likely contains the true value of an unknown population parameter.
Standard Error
The standard deviation of the sample distribution of a statistic, often used in the context of mean.
Mean
The central or typical value in a distribution, calculated as the sum of all observations divided by the number of observations.
- Ascertain precise confidence intervals from sample statistics.
Verified Answer
CI = X̄ ± (Zα/2 x SE)
Where X̄ is the sample mean, SE is the standard error of the mean, and Zα/2 is the critical value of the standard normal distribution for the given confidence level (90% in this case).
Substituting the given values, we get:
CI = 137.98 ± (1.645 x 4.98)
Calculating the values, we get:
CI = (129.51, 146.45)
Therefore, the best choice is A.
Learning Objectives
- Ascertain precise confidence intervals from sample statistics.
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