## 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
• 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)
• (1-α) 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

• 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 z-values 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 This site uses Akismet to reduce spam. Learn how your comment data is processed. 