A survey collects demographic, socioeconomic, dietary, and health-related inform

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 ts value, the lower the risk for heart disease) 35 49 51 54 65 51 52 47 87 37 46 33 39 44 39 64 94 34 30 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. Need Help? Talk to a Tutor

Explanation / Answer

Solution:- Given that information : 35,49,51,54,65,51,52,47,87,37,46,33,39,44,39,64,94,34,30,48

a) population mean = sum of terms/no of terms
= 999/20
= 49.95

b) The point estimate of the value that separates the largest 50% and the smallest 50% of HDL level is defined as the median of the cholesterol level

=> The median of the data set is 47.5.

Explanation
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:
30 33 34 35 37 39 39 44 46 47 48 49 51 51 52 54 64 65 87 94

As you can see, we do not have just one middle number but we have a pair of middle numbers,
so the median is the average of these two numbers:

Median = (47+48)/2=47.5

c) the population standard deviation : 16.851

d) P(X > 60) = P(Z > (60 - 49.95)/(16.81/sqrt(20)) )
= P(Z > 2.6737)
= 0.0038

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