Estimators and Estimates
 An Estimator is a mathematical function approximates a population parameter depending on sample information.
 Estimators have two important properties
 Bias:
 The expected value of an unbiased estimator is the population parameter. The bias in this case is zero
 If the expected value of an estimator is (parameter+b), then the bias is b.
 Efficiency:
 The most effecient estimator is the one with smallest variance
 Bias:
 Estimates:
 An estimate is the output that you get from estimator (when you apply some formula).
 There are two types of estimates
 Point Estimate:
 A single value
 Examples:
 1
 5
 10000
 122.47
 0.32
 Confidence Interval:
 An interval
 Example:
 (0,3)
 (4,8)
 (9050, 10050)
 (0.70, 0.56)
 A confidence interval is an interval within whic we are confident (with a certain percentage of confidence) the population parameter will fall.
 Example: You have visited to 5% of the restaurants in hyderbad and found from the sample the average price of biryani is 225 Rs. So now you are 95% confident that the average biryani price in hyderabad will be in the range of (180, 275)
 (1α) is the level of confidence
 If we want 90% confidence α = 10% => 0.1
 If we want 95% confidence α = 5% => 0.05
 If we want 99% confidence α = 1% => 0.01 Calculating Confidence Interval
 Point Estimate:

While calculating confidence intervals we have two different situations
 Known Population Variance
 Unknown Population Variance

Lets Go with Known Population Variance:
 General formula

Consider the following xls which zvalues Refer Here

Lets consider the following data set which has data scientist salaries sample. Since we are using Estimations with known variance. Std dev of the population $15000. Refer Here

Lets calculate the sample mean and standard error

Lets calculate the Confidence intervals with 99% confidence and then 95% confidence
 α = 1% => 0.01
 α/2 => 0.005

Calculate Confidence intervals with 90% confidence