Question

5. Northern Orange County has found that the population has a severe problem with dental plaque. Every year the local dental board examines a sample of patients and rates each patient's plaque buildup on a scale from 1 to 100, with 1 representing no plaque and 100 representing a great deal of plaque. This year, the board examined 21 patients and found that they had an average (x̄̄) Plaque Rating Score (PRS) of 72 and a standard deviation (s) of 6.2. Construct a 98 percent confidence interval for the mean PRS for Northern Orange County

Answer 1

5) 98% confidence interval for population mean PRS     
Given     
X̅ = 72  Sample Mean   
σ = 6.2  Population Standard Deviation   
n = 21  Sample Size   
Confidence interval for mean is given by  

For 98%, α = 0.02, α/2 = 0.01      
From the z-tables, or Excel function NORM.S.INV(α/2)      
z = NORM.S.INV(0.01) = 2.326   (We take the positive value for calculations)  

      = (68.85, 75.15)   (Rounding to two decimals)  
      
98% confidence interval is (68.85, 75.15)