Standard Error and a Confidence Interval
~12 mincode completion
Implement mean_confidence_interval(x, z) returning [low, high], a two-element list.
Use the unbiased sample standard deviation (ddof=1).
Examples
Four evenly spaced points, at roughly 95% confidence
- Input
- mean_confidence_interval([2, 4, 6, 8], 1.96)
- Output
- [2.46965, 7.53035]
A sample with no spread gives an interval of zero width
- Input
- mean_confidence_interval([3, 3, 3], 1.96)
- Output
- [3, 3]
A wider multiplier gives a wider interval around the same mean
- Input
- mean_confidence_interval([1, 2, 3, 4, 5], 2.58)
- Output
- [1.17566, 4.82434]
Hints
Hint 1
Take the square root at the end, not inside the sum.
Hint 2
A common slip here: uses the standard deviation instead of the standard error.
Requirements
x: array of observations, shape (n,)z: multiplier, e.g. 1.96 for roughly 95%Return list of two floats: [lower bound, upper bound]
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
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Where this shows up
~12 min
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Python
import numpy as np
def mean_confidence_interval(x, z):
"""
A z-based confidence interval for the sample mean.
Args:
x: array of observations, shape (n,)
z: multiplier, e.g. 1.96 for roughly 95%
Returns:
list of two floats: [lower bound, upper bound]
"""
# YOUR CODE HERE
pass