- Asked 2/17
- 2075 Asoj · 6 marks
Sampling distribution: population 2,8,14,20
Short answer
Population 2,8,14,20 has mean 11. The six possible samples of size two without replacement have means 5,8,11,11,14,17, whose mean is 66/6=11, equal to the population mean.
A population consists of four number 2, 8, 14, 20. a) Write down all possible sample size of two without replacement. b) Verify that the population mean is equal to the mean of the sample mean.
Population: 2, 8, 14, 20 (N = 4), n = 2, without replacement, number of samples = ⁴C₂ = 6.
a) All possible samples
| No. | Sample | Sample mean |
|---|---|---|
| 1 | (2, 8) | 5 |
| 2 | (2, 14) | 8 |
| 3 | (2, 20) | 11 |
| 4 | (8, 14) | 11 |
| 5 | (8, 20) | 14 |
| 6 | (14, 20) | 17 |
b) Population mean equals mean of sample means
Population mean: μ = (2 + 8 + 14 + 20)/4 = 44/4 = 11
Sum of sample means = 5 + 8 + 11 + 11 + 14 + 17 = 66
Mean of sample means = 66/6 = 11
Hence mean of the sample means (11) = population mean (11). Verified.
✓ Answer checked by Claude Sonnet 5.5
Related questions
- Samples of 2,8,14,20 with standard error · Probability and Statistics, chapter 4 · asked 2×
- Sampling distribution: population 4,8,12,16,20 · Probability and Statistics, chapter 4
- Sampling distribution: population 2,4,6,8 · Probability and Statistics, chapter 4
- Sampling distribution: population 5,6,9,12 · Probability and Statistics, chapter 4
- Standard error; population 12,19,13,16 · Probability and Statistics, chapter 4
- Population, parameter, statistic; samples of 3,7,11,15 · Probability and Statistics, chapter 4
- Sampling distribution of mean; standard error · Probability and Statistics, chapter 4 · asked 2×
- Number and size of RSF, 1,20,000 population · Water Supply Engineering, chapter 6
- Replacement strategy for four-year need · Engineering Economics, chapter 5
- Verify suggested discharge distribution (Hardy Cross) · Hydraulics, chapter 3
- Capacitor size, feeder with three equal loads · Transmission and Distribution System Design, chapter 7