Mathematics, 03.07.2020 16:01 trinidydavis

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 51 54 65 51 52
47 87 37 46 33 39 44
39 64 94 34 30 48

Requried:
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.

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Answer from: ellisc7044

(a) The point estimate of the population mean HDL cholesterol level is 49.95.

(b) The point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is 47.5.

Step-by-step explanation:

We are given a sample of 20 observations on HDL cholesterol level (mg/dl) obtained from the survey below;

35, 49, 51, 54, 65, 51, 52, 47, 87, 37, 46, 33, 39, 44, 39, 64, 94, 34, 30, 48.

(a) The point estimate of the population mean HDL cholesterol level is given by the sample mean of the above data, i.e;

Sample Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{35+ 49+ 51+ 54 +65 +51+ 52+ 47+ 87+ 37+ 46+ 33+ 39+ 44+ 39+ 64+ 94+ 34+ 30+ 48}{20}$

= $\frac{999}{20}$ = 49.95

So, the point estimate of the population mean HDL cholesterol level is 49.95.

(b) The point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is given by the Median of the above data.

Firstly, arranging the given data in ascending order we get;

30, 33, 34, 35, 37, 39, 39, 44, 46, 47, 48, 49, 51, 51, 52, 54, 64, 65, 87, 94.

Now, for calculating median we have to first observe that the number of observations (n) in our data is even or odd, i.e;

If n is odd, then the formula for calculating median is given by;

Median = $(\frac{n+1}{2})^{th} \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}$

Here, the number of observations is even, i.e. n = 20.

So, Median = $\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}$

= $\frac{(\frac{20}{2})^{th} \text{ obs.}+(\frac{20}{2}+1)^{th} \text{ obs.} }{2}$

= $\frac{(10)^{th} \text{ obs.}+(11)^{th} \text{ obs.} }{2}$

= $\frac{47+48 }{2}$

Median = 47.5

Hence, the point estimate of the value that separates the largest 50% of HDL levels from the smallest 50% is 47.5.

Standard deviation, s = $\sqrt{\frac{\sum(X-\bar X)^{2} }{n-1} }$

= $\sqrt{\frac{ (30-49.95)^{2}+(33-49.95)^{2}+(34-49.95)^{2}+........+(94-49.95)^{2}}{{20-1}} }} }$

= 16.85

Answer from: Quest

You would need a laid out graph for this but could you provide a picture of just a graph? i can give stepssolve for y.subtract 4xdivide by -1 (opposites)graph slope intercept formcheck each point to see if it’s on the graph

Answer from: Quest

the 3rd on is correct

step-by-step explanation:

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