- 2075 Asoj · 3+3 marks
Point vs interval estimation; estimation vs testing
Short answer
Point estimation gives a single value; interval estimation provides a range with confidence level. Estimation finds parameter values; hypothesis testing decides whether a claim about a parameter is supported by sample evidence.
What are the difference between point estimation and Interval estimation? Also discuss differences between estimation and Hypothesis testing.
Point estimation vs interval estimation
| Basis | Point estimation | Interval estimation |
|---|---|---|
| Meaning | A single sample value is used to estimate the parameter | A range of values is given that is expected to contain the parameter |
| Example | x̄ = 56 estimates μ | 54.7 < μ < 57.3 |
| Reliability | No information about accuracy or error | Gives a stated confidence level (95%, 99%) |
| Precision | Rarely equal exactly to the parameter | Width shows the precision of the estimate |
| Based on | Estimator (x̄, s², p̂) | Estimator, standard error and a table value: x̄ ± Z·SE |
| Use | Quick, simple estimate | More informative, preferred in practice |
Estimation vs hypothesis testing
| Basis | Estimation | Hypothesis testing |
|---|---|---|
| Aim | To find the value of an unknown parameter | To decide whether a claim about a parameter is true |
| Starting point | No prior assumption about the parameter | A hypothesis (H₀ and H₁) is set up first |
| Result | A value or an interval (confidence interval) | Decision to reject or not reject H₀ |
| Error measure | Confidence level (1 − α), margin of error | Type I error α and Type II error β |
| Question answered | "What is the value of μ?" | "Is μ equal to 50?" |
| Tools | Estimator, standard error, confidence limits | Test statistic, critical region, p-value |
The two are related: a (1 − α) confidence interval can be used for a two-tailed test at level α. If the hypothesised value lies outside the interval, H₀ is rejected.
✓ Answer checked by Claude Sonnet 5.5
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