Exercise · ZW-SAMPLE-MEAN-010 · ★★★ Advanced
What is the difference between \(\bar X\) and \(\mu\)?
Choose one option.
Show answer
- D. \(\mu\) is a fixed parameter; \(\bar X\) changes from sample to sample
Explanation
\(\mu\) is a population constant; \(\bar X\) is a random variable that varies with the sample, with \(E[\bar X]=\mu\).
Review the concept: Sample mean
The sample mean \(\bar X\) is the arithmetic average of the \(n\) variables \(X_i\) of a random sample; since it depends on the sample, it is itself a random variable.
\[\bar X=\dfrac{1}{n}\sum_{i=1}^{n}X_i\]
More practice problems: sample mean
- ZW-SAMPLE-MEAN-001 The sample data are 2,\ 4,\ 6,\ 8. What is the sample mean?
- ZW-SAMPLE-MEAN-002 The data are 3,\ 7,\ 5,\ 9,\ 6. What is bar x?
- ZW-SAMPLE-MEAN-003 A random sample of size 25 comes from a population with mean μ=10. What is E[bar X]?
- ZW-SAMPLE-MEAN-004 A sample of size 9 comes from a population with variance σ^2=36. What is Var(bar X)?
- ZW-SAMPLE-MEAN-005 With σ=10 and n=25, what is the standard deviation of bar X?
- ZW-SAMPLE-MEAN-006 To halve the standard deviation of the sample mean, the sample size must be multiplied by:
- ZW-SAMPLE-MEAN-007 For the data 1,\ 2,\ 6, what do the deviations x_i-bar x add up to?
- ZW-SAMPLE-MEAN-008 The mean of 10 observations is 12. One more observation of 23 is added. What is the new mean?