-- Confidence Intervals

-- Data values
values = [41,40,36,26,27,37,45,47] :: [Double]

-- T-table value
t = 2.13145 :: Double


-- Change the input values and *POFF* the answers appear
ci :: IO ()
ci = do let a1 = lower mean t deviation n
        let a2 = higher mean t deviation n
        putStrLn ""
        putStrLn $ "N:    " ++ show n
        putStrLn $ "Mean: " ++ show mean
        putStrLn $ "Var:  " ++ show variance
        putStrLn $ "S D:  " ++ show deviation
        putStrLn ""
        putStrLn $ "Low:  " ++ show a1
        putStrLn $ "High:  " ++ show a2
        
-- Useful functions using the data values
n = fromIntegral $ length values :: Double
mean = (sum values) / n
variance = sum $ map (\x->(x-mean)^2 / (n-1)) values
deviation = sqrt(variance)

-- Lower and higher functions
lower :: Double -> Double -> Double -> Double -> Double
lower mean tvalue deviation n = mean - ((tvalue * deviation) / (sqrt(n)))

higher :: Double -> Double -> Double -> Double -> Double
higher mean tvalue deviation n = mean + ((tvalue * deviation) / (sqrt(n)))