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

answer: the answer is one of

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

step-by-step explanation: we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

Answer from: Quest

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: