Point estimation

Inferential Statistics
Making statements about a population by examining sample results
Sample statistics
(known)

Population parameters
Inference

(unknown, but can be estimated from sample evidence

Sample

Population

Sample Statistics as Estimators of
Population Parameters
A sample statistic is a numerical measure of a summary characteristic of a sample. •
•
•

A population parameter is a numerical measure of a summary characteristic of a population. An estimator of a population parameter is a sample statistic used to estimate or predict the population parameter.
An estimate of a parameter is a particular numerical value of a sample statistic obtained through sampling.
A point estimate is a single value used as an estimate of a population parameter.

Inferential Statistics
Drawing conclusions and/or making decisions concerning a population based on sample results.

• Estimation
Estimate the population mean using the information derived from sample

• Hypothesis Testing
Use sample evidence to test hypotheses about the population mean

Point and Interval Estimates
• A point estimate is a single number,
• A confidence interval contains a certain percentage of possible values of the parameter

Lower
Confidence
Limit

Point Estimate
Width of confidence interval

Upper
Confidence
Limit

Point Estimates
Estimate Population
Parameters …

with Sample
Statistics

Mean

µ

X

Proportion

p

PS

Variance
Difference

σ

2

µ1 − µ 2

S

2

X1 − X 2

Point Estimate
Table 1.1 : Annual salary and training programme status
Sl
No

Annual
Salary

Mgt
Training

Sl No

Annual
Salary

Mgt
Training

1

49,094.30

Yes

16

51,766.00

Yes

2

53,263.90

Yes

17

52,541.30 No

3

49,643.50

Yes

18

44,980.00

Yes

4

49,894.90

Yes

19

51,932.60

Yes

5

47,621.60 No

20

52,973.00

Yes

6

55,924.00