Question

A survey collects demographic, socioeconomic, dietary, and health-related information on an annual basis. Here is a sample of 20 observations on HDL cholesterol level (mg/dl) obtained from the survey (HDL is "good" cholesterol; the higher its value, the lower the risk for heart disease). 35 49 52 54 66 50 50 47 85 37 46 34 39 44 39 62 95 35 31 48 (a) Calculate a point estimate of the population mean HDL cholesterol level. (b) Making no assumptions about the shape of the population distribution, calculate a point estimate of the value that separates the largest 50% of HDL levels from the smallest 50%. (c) Calculate a point estimate of the population standard deviation. (Round your answer to three decimal places.) (b) An HDL level of at least 60 is considered desirable as it corresponds to a significantly lower risk of heart disease. Making no assumptions about the shape of the population distribution, estimate the proportion p of the population having an HDL level of at least 60. p =

Answer 1

S.No (X-X) 31.000 -18.900 34.000 - 15.900 35.000 -14.900 35.000 - 14.900 37.000 -12.900 39.000 - 10.900 39.000 - 10.900 44.000 -5.900 46.000 -3.900 47.000 -2.900 48.000 -1.900 49.000 -0.900 50.000 0.100 50.000 0.100 52.000 2.100 54.000 4.100 62.000 12.100 66.000 16.100 85.000 35.100 95.000 45.100 998 49.900 5+=(x-x)+/(n-1)= S=Vs? 357.2100 252.8100 222.0100 222.0100 166.4100 118.8100 118.8100 34.8100 15.2100 8.4100 3.6100 0.8100 0.0100 0.0100 4.4100 16.8100 146.4100 259.2100 1232.0100 2034.0100 5213.8000 274.4105 16.5653 X=Ex/n

a)

point estimate of the mean value =Σxi/n =

49.9000

b)

point estimate of median =middle value=

47.5

c)

estiamted population standard deviation s =

16.565

d)

proportion of values at least 60 =x/n=4/20 =

0.2