Question

Differentiate Confidence Interval as an estimation method from Interval as a level of measurement in descriptive statistics. Give an example of each Confidence Interval and Interval.

Answer 1

THE CONFIDENCE INTERVAL IS THE ACTUAL UPPER AND LOWER BOUNDS OF THE ESTIMATE YOU EXPECT TO FIND AT A GIVEN LEVEL OF CONFIDENCE.

FOR EXAMPLE, IF YOU ARE ESTIMATING A 95% CONFIDENCE INTERVAL AROUND THE MEAN PROPORTION OF FEMALE BABIES BORN EVERY YEAR BASED ON A RANDOM SAMPLE OF BABIES, YOU MIGHT FIND AN UPPER BOUND OF 0.56 AND A LOWER BOUND OF 0.48. THESE ARE THE UPPER AND LOWER BOUNDS OF THE CONFIDENCE INTERVAL. THE CONFIDENCE LEVEL IS 95%.

THIS MEANS THAT 95% OF THE TIME, YOU CAN EXPECT YOUR ESTIMATE TO FALL BETWEEN 0.56 AND 0.48.

CONFIDENCE INTERVAL IS ALWAYS IN THE SAME UNIT AS THE POPULATION PARAMETER OR SAMPLE STATISTIC. CONFIDENCE INTERVAL IS GENERATED/CALCULATED USING THE CONFIDENCE LEVEL REQUIRED BY THE USER WITH THE HELP OF Z TABLE/T TABLE/CHI-SQUARE TABLE BASED ON THE DISTRIBUTION.

IT IS THE PROBABILITY THAT THE POPULATION PARAMETER VALUE LIES BETWEEN A SPECIFIED ‘RANGE’. THIS SPECIFIED RANGE (21S TO 25S) IS THE CONFIDENCE INTERVAL. CONFIDENCE INTERVAL IS ALWAYS EXPRESSED IN PERCENTAGE AND MOST OF THE STATISTICAL CALCULATIONS USE A VALUE OF 95% OR 99%, DEPENDING UPON THE ACCURACY OF DATA NEEDED.

INTERVAL ESTIMATION IS THE USE OF SAMPLE DATA TO CALCULATE AN INTERVAL OF POSSIBLE (OR PROBABLE) VALUES OF AN UNKNOWN POPULATION PARAMETER, IN CONTRAST TO POINT ESTIMATION, WHICH IS A SINGLE NUMBER.

INTERVAL ESTIMATION IS THE USE OF SAMPLE DATA TO CALCULATE AN INTERVAL OF POSSIBLE (OR PROBABLE) VALUES OF AN UNKNOWN POPULATION PARAMETER, IN CONTRAST TO POINT ESTIMATION, WHICH IS A SINGLE NUMBER.

Μ=X¯±ZΑ2ΣN√

· X¯X¯ = MEAN

· ZΑ2ZΑ2= THE CONFIDENCE COEFFICIENT

· ΑΑ= CONFIDENCE LEVEL

· ΣΣ= STANDARD DEVIATION

· NN= SAMPLE SIZE